In a Biblical sense Exegesis is a theological term used to describe an approach to interpreting a passage in the Bible by critical analysis. In contemporary usage, it can mean a critical explanation or interpretation of any text, whether in the Bible or not.
Proper exegesis includes using the context around the passage, comparing it with other parts of the Bible, and applying an understanding of the language and customs of the time of the writing, in an attempt to understand clearly what the original writer intended to convey. In other words, it is trying to "pull out" of the passage the meaning inherent in it. The opposite of exegesis is eisegesis, which is an approach to interpreting a Bible passage by reading into it a meaning that is not evident at all by the passage.
There exist at least two different forms or type of exegesis - revealed and rational. Revealed believes the Holy Spirit inspired the Biblical authors of the texts and therefore the words in the Bible convey God's divine revelation to man. Rational believes that the original writers of the Bible's books used their own creativity and inspiration (apart from God) to write what they did. In short, some study the Bible believing that God himself directly inspired its writers while others approach the Bible as a collection of stories, fables, myths, etc. brought to life through the creativity and imagination of man.
The Bible itself, however, clearly states its writers were inspired and even eyewitnesses to what they wrote. Rather than being a collection of fanciful fables or stories created out of the will of man, the Bible teaches its words came from God to holy men and women through the power of the Holy Spirit:
"For we DID NOT follow cunningly devised fables when we made known to you the power and coming of our Lord Jesus Christ, but were eyewitnesses of His majesty. For He received from God the Father honor and glory when such a voice came to Him from the Excellent Glory: 'This is My beloved Son, in whom I am well pleased.' And we heard this voice which came from heaven when we were with Him on the holy mountain.
"And so we have the prophetic word confirmed, which you do well to heed as a light that shines in a dark place, until the day dawns and the morning star rises in your hearts; knowing this first, that no prophecy of Scripture is of any PRIVATE interpretation, for prophecy NEVER came by the will of man, but holy men of God spoke as they were moved by the Holy Spirit." (2Peter 1:16-21, NKJV)