The following explanation of this term is from Meditate In Thy Precepts:
In Ephesians 6:17b we see, "...and the sword of the Spirit, which is the word of God." The word translated "word" is rhema, which is a Greek term describing individual phrases or passages in a literary work. Paul did not use logos, a term describing often the general summation of the Scripture, but rather rhema, describing more properly each individual passage in the Scripture, each verse that can, in one circumstance or another, be used to counteract a lie from satan. When the Lord was tempted of satan in the desert, He didn't just remind the enemy that God's logos says "this general refutation of your temptation". Rather, He quoted specific passages that uniquely dealt with the temptation at hand, and thus contrafuted and defeated the tempter.
Another good explanation is taken from What Is Truth (this blog entry is well worth the read, explaining the meaning of the term Paul used in 2 Timothy 2:15, "rightly dividing the word of truth"):
The message of God's Word works powerfully in its context. Romans 10:17 says that faith comes by hearing and hearing by the Word of God. "Word" there is the Greek word rhema. Rhema is not the Greek term for all of the Bible. Rhema speaks of a portion of the Word of God, a piece of God's Word that deals with a particular point of doctrine and practice, seen within an appropriate conception of its context... Our faith comes from seeing passages in their context and understanding them as the Lord intended.
As a brand new believer, I remember witnessing to the lost and fellowshipping with the saved, speaking about anything from the Bible, thinking that would be a benefit to others - and it never seemed to get anyone saved, and it certainly didn't strengthen anyone's faith. But then later, when I learned what passages (and facts) specifically to cover when presenting the Gospel or teaching a particular Bible study, I found that God's Word had an impact on their lives. The lost came under conviction through the presenting of the Gospel of Christ (rather than just discussing God's Word in general - that's where I was as a new believer, wanting to talk about everything, but not building precept upon precept), and believers were strengthened in their faith - when they saw something specific in the Word of God, when they saw something layed out systematically before them.
According to those definitions above, faith comes when we believe and apply specific portions of God's Word to our lives. It is not just reading in general - though that is beneficial - but studying out each specific theme or passage that builds our faith. If we want faith, for example, about how God answers prayer, reading just any passage is not going to help us in this area - but reading passages specifically about prayer, seeing examples of God doing this in Scripture, will do so.
For some examples, notice how the following passages show that it was a specific word that was brought to mind or referred to:
Mark 14:72 And the second time the cock crew. And Peter called to mind the word that Jesus said unto him, Before the cock crow twice, thou shalt deny me thrice. And when he thought thereon, he wept.
Luke 2:26, 28-30 And it was revealed unto him by the Holy Ghost, that he should not see death, before he had seen the Lord's Christ. Then took he him up in his arms, and blessed God, and said, Lord, now lettest thou thy servant depart in peace, according to thy word: For mine eyes have seen thy salvation.
Luke 2:49-50 And he said unto them, How is it that ye sought me? wist ye not that I must be about my Father's business? And they understood not the saying which he spake unto them. (Here the word "saying" is the word rhema.)
Luke 5:4-5 Now when he had left speaking, he said unto Simon, Launch out into the deep, and let down your nets for a draught. And Simon answering said unto him, Master, we have toiled all the night, and have taken nothing: nevertheless at thy word I will let down the net.
Luke 1:35-38 And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God. And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the sixth month with her, who was called barren. For with God nothing shall be impossible. And Mary said, Behold the handmaid of the Lord; be it unto me according to thy word. And the angel departed from her. (In this passage, the word rhema is used twice in reference to God's specific promise/statement that Mary would bear the Messiah, through the miracle of the virgin birth. The word "nothing" here is also the word rhema - this verse is indicating that nothing - that God has said or promised specifically - would be impossible to Him. The Lord keeps His promises to us! If we claim His promises and do our part, the Lord will surely do His! When we pray according to God's will - which means according to the Word of God - nothing He has said will be impossible, but will instead be fulfilled.)
Luke 24:6-8 He is not here, but is risen: remember how he spake unto you when he was yet in Galilee, Saying, The Son of man must be delivered into the hands of sinful men, and be crucified, and the third day rise again. And they remembered his words.
John 12:47-48 And if any man hear my words, and believe not, I judge him not: for I came not to judge the world, but to save the world. He that rejecteth me, and receiveth not my words, hath one that judgeth him: the word that I have spoken, the same shall judge him in the last day. (Here Jesus is speaking to the multitude, referring to specific sayings He has told them in His testifying to them - but then He states that if they refuse to heed His words - rhema - and get saved, they will be judged by His Word - logos, referring to the entirety of the Word of God.)
2 Peter 3:1-2 This second epistle, beloved, I now write unto you; in both which I stir up your pure minds by way of remembrance: That ye may be mindful of the words which were spoken before by the holy prophets, and of the commandment of us the apostles of the Lord and Saviour: (Specific words being referred to.)
Jude 1:17-18 But, beloved, remember ye the words which were spoken before of the apostles of our Lord Jesus Christ; How that they told you there should be mockers in the last time, who should walk after their own ungodly lusts.
Notice in the following passages that it is specifically the Gospel (the good news of salvation) that was being referred to, not the whole Word of God in general:
John 6:63 It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life.
John 6:68 Then Simon Peter answered him, Lord, to whom shall we go? thou hast the words of eternal life.
Acts 5:20 Go, stand and speak in the temple to the people all the words of this life.
Acts 10:22 And they said, Cornelius the centurion, a just man, and one that feareth God, and of good report among all the nation of the Jews, was warned from God by an holy angel to send for thee into his house, and to hear words of thee.
Acts 11:14 Who shall tell thee words, whereby thou and all thy house shall be saved.
Romans 10:8 But what saith it? The word is nigh thee, even in thy mouth, and in thy heart: that is, the word of faith, which we preach; That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.
1 Peter 1:25 But the word of the Lord endureth for ever. And this is the word which by the gospel is preached unto you.
To cap off this study, here are some specific words we need:
1) Words to live by:
Matthew 4:4 But he answered and said, It is written, Man shall not live by bread alone, but by every word that proceedeth out of the mouth of God.
Yes, we need the whole Word of God - but we live by each daily portion. If we want to overcome the devil in our day to day spiritual battles, we need to do what Jesus did in His temptation in the wilderness: He quoted specific passages of Scripture that refuted the temptations of Satan. All three passages that Jesus quoted were from the book of Deuteronomy, and each one specifically addressed what the devil was saying.
2) Words to fight our spiritual battles by:
In Jesus' example, we see the sword of the Spirit (the Word of God) in action:
Ephesians 6:17 And take the helmet of salvation, and the sword of the Spirit, which is the word of God:
This is an active use of the Word of God - offensively using passages of Scripture (specific portions) in our witnessing, in resisting the devil, in fighting temptation, in exhorting our brethren; whereas the shield of faith (see next point) is defensively using the Bible to stop the devil's lies, temptations and slanders - his fiery darts - from taking lodge in our hearts and minds. In both cases, we need specific portions of the Word of God - portions that address the particular battle we are facing.
3) Words to trust by:
Romans 10:17 So then faith cometh by hearing, and hearing by the word of God.
It is specific passages and portions that will increase our faith in each area of our lives. For example, if we want to grow in our faith in the area of God's provision in our lives, we need to study out passages, promises, and principles dealing particularly with that.
4) Words to pray by:
John 15:7 If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you.
Specific portions of the Word of God that applied to the particular request being prayed for. If we want to pray according to God's will (and therefore be assured that our requests will be answered - see 1 John 5:14-15), we first need to dig into the Word of God and find passages that teach us what His will is in each area we are praying for.
5) Words to cleanse our lives by:
Ephesians 5:26 That he might sanctify and cleanse it with the washing of water by the word.
Here we see that it is specific passages that cleanse us in our daily walks with the Lord. As James 1:22-25 refers to, we need to see our sin and the solution, then apply those specific passages to our lives - and God says His Word will cleanse us.
Are you living by the Word (rhema) of God - living each day by specific passages, taking and applying to your life each portion that particularly addresses it? Fighting your battles and using both the Sword of the Spirit and the shield of faith to protect yourself against specific attacks and wiles of the Devil? Building your faith by digging in the Bible and clinging to certain promises? Praying according to particular passages? And cleansing your heart and conduct by what God has revealed in His Word?