Exegesis

Exegesis is the formal, critical interpretation of a text, especially religious scripture. It is when, through the study of the cultural context for which religious texts are written, and the meanings of the words within context, that the intended meaning of the writings can be exposed. Instead of subjectively bringing one's own interpretation into the texts when analyzing them, the idea is to interpret it as objectively as possible.

Answers in Genesis has an example of exegesis in action, from Genesis 1:

"In Genesis 1, the Hebrew word for day (yôm), as used for each of the six Days of Creation, would be looked at in regard to context and the type of literature. Genesis is written in typical Jewish historical narrative—this is important to understand when interpreting the words of this book. Any reputable Hebrew lexicon (one-way dictionary) will list the different meanings given to a word (like ‘day’), and the various contexts that determine these meanings. One will find that whenever the yôm (day) is qualified by a number or the phrase evening and morning, it always means an ordinary day. Thus, critically looking at the text and then reading out of Scripture, one cannot come to any other conclusion except that these days were ordinary (24-hour) days.''"

Claims as to what exegesis can reveal, for instance Genesis 1, can vary wildly, from revealing that the Bible indicates that the world was created in 6 days, to that exegesis reveals that there's no disparity between Genesis 1, and what Science has shown. Clearly, from AiG's exegesis above, there's little in common of Genesis 1 and Science, in this case.

Bias in Interpretation
Ultimately, exegesis claims need to be critically examined. Because someone claims to have practice exegesis, and come up with a particular interpretation, does not mean he/she is correct or unbiased. For example of that bias, Answers in Genesis continues:

"When church members and their subsequent generations are trained in this method of thinking (interpreting Scripture in context), they have a respect for God’s Word and then judge the ‘world’s’ fallible theories on the basis of what the Word of God clearly states. When they are taught to use exegesis in Genesis, they usually consistently apply this method of interpretation throughout the rest of the Bible. They have a solid faith in absolute truth. Especially when they then see how, starting with the history given in the Bible, they can make better sense of the same evidence which was previously used to undermine the Bible. They are not tossed ‘to and fro’ by the world’s fallible ideas, but by and large stand firm on the authoritative Word."

Bias isn't always a bad thing. Bias towards the truth, for example, is healthy. When the purpose of exegesis, however, is to be as unbiased as possible, any amount of bias is going to radically alter the interpretation to be in favor of what the examiner wants. This is why verifying and peer reviewing the claims is as important as it is in science.