When Christians say that the Bible is inspired, they are saying that it is "God breathed." 2 Tim. 3:16-17 says, "All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness; 17 that the man of God may be adequate, equipped for every good work." The word for "inspired" is the Greek θεόπνευστος, "theopneustos," which means "God breathed." In other words, this means that the Scriptures are authored from God and that God moved through the personality and abilities of the Biblical writers in such a way that what they wrote was without error and was correct in everything that it addressed. Therefore, the Scriptures are the product of both God and man, and the Scriptures reflect the writing style of different individuals.
This process of inspiration was not a mechanical dictation where the writer simply wrote down what was heard. Neither did they go into a trance like some cases of "automatic writing" which are said to occur in occult practices. Instead, the writers of the Bible were free to write what they wanted, the way they wanted, and when they wanted; yet it was God moving through them to ensure the integrity and accuracy of what was said.
Furthermore, the Christian church recognizes the inspired Scriptures because the Holy Spirit who indwells believers recognizes the voice of God. The church did not give us the Scriptures. The Christian church recognized the Christian Scriptures.