Faithful means "true to one's word. Constant; not fickle." It carries the idea of being trustworthy, dependable, reliable. Over and over in the Scriptures, God and His Word are both declared to be faithful.
There are some specific things that God is declared to be faithful about:
1) Faithful to give us a way out of the temptations we face in life.
1 Corinthians 10:13 There hath no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it.
2) Faithful to forgive us when we repent and confess our sins to Him.
1 John 1:9 If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
3) Faithful to give us new mercies every morning.
Lamentations 3:22-23 It is of the LORD'S mercies that we are not consumed, because his compassions fail not. They are new every morning: great is thy faithfulness.
4) Faithful to deliver us from evil.
2 Thessalonians 3:1-3 Finally, brethren, pray for us, that the word of the Lord may have free course, and be glorified, even as it is with you: And that we may be delivered from unreasonable and wicked men: for all men have not faith. But the Lord is faithful, who shall stablish you, and keep you from evil.
5) Faithful to keep His promises and to always be our High Priest on the throne of grace.
Hebrews 10:19-25 Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus, By a new and living way, which he hath consecrated for us, through the veil, that is to say, his flesh; And having an high priest over the house of God; Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water. Let us hold fast the profession of our faith without wavering; (for he is faithful that promised;) And let us consider one another to provoke unto love and to good works: Not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another: and so much the more, as ye see the day approaching.
6) Faithful to be faithful! - even when we struggle with doubt.
2 Timothy 2:11-13 It is a faithful saying: For if we be dead with him, we shall also live with him: If we suffer, we shall also reign with him: if we deny him, he also will deny us: If we believe not, yet he abideth faithful: he cannot deny himself.
There are three things the Word of God tells us that God cannot do. The first was mentioned above - God cannot deny Himself. He is not double-minded; He meant exactly what He said.
The second one is: God cannot be tempted with evil (ie. sin).
James 1:13 Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man:
He will never turn aside from His righteousness or holiness. He will always be the same; He will never change or be corrupted in any way - unlike faithless man.
The third thing is: God cannot lie.
Titus 1:2 In hope of eternal life, which God, that cannot lie, promised before the world began;
That means that God will be faithful to all He has promised, faithful to keep His Word, faithful to His covenants, faithful to His children.
7) Faithful to preserve His children and to continue the work that He has begun in us.
1 Thessalonians 5:23-24 And the very God of peace sanctify you wholly; and I pray God your whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ. Faithful is he that calleth you, who also will do it.