Inspiration is the doctrine that the Bible was written by the influence of God and is without error in the original documents. It is accurate and authoritatively represents God's teachings (2 Tim. 3:16) as well as historical events including the sins of people and the works of the demonic realm. As such it is a revelation from God which implies direct knowledge about God, creation, man, salvation, the future, etc. It is an illumination in that it shows us what we could not know apart from it.
One of the ways to prove that the Bible is inspired is to examine the O.T. prophecies fulfilled in the New Testament concerning Jesus (Luke 24:27-45). Because the Bible is inspired, its words are unbreakable (John 10:34-36), eternal (Matt. 24:35), trustworthy (Psalm 119:160), and able to pierce the heart of man (Heb. 4:12). Additionally, the inspired Word of God will not go forth without accomplishing what God wishes it to (Isaiah 55:11).
There is concursive inspiration which says that God's power worked with human personalities and did not override them.
Dictation inspiration says that the writers of the Bible wrote exactly what was given to them by the Holy Spirit.
Dynamic inspiration is the position that the Holy Spirit worked through the writers by providing guidance and the writers chose whatever phraseology they wanted to to convey those ideas.
Organic inspiration says that the Holy Spirit used the author's personality, abilities, and giftings in writing the documents so that individual styles of different writers are clearly seen.
Plenary inspiration says that the whole Bible is inspired--not just parts. Plenary means "full."
Verbal inspiration means the Holy Spirit guided the exact words that the authors were to use when composing their writings.