Dictionary.com & Etymonline.com
It is all that explains and interprets the Holy Scriptures in the study of theology.
This area of study involves the study of ancient languages like Greek, Hebrew, and Aramaic in order to study the Scriptures from primary sources – the original/early manuscripts of the Bible.
This also includes archeology and study of the canon of Scripture. Archeology in the study of ancient cultures and people surround the original writings. Canon in the study of the process involved in bringing the various books of the Bible together into the Bible as we know it today which was also against a historical background.
Exegetical theology therefore also includes criticism of the Scriptures and, by relation, the interpretation. This probably becomes obvious to you as you stop to think about what would be logically involved in the above-mentioned elements.
In the end, this is a very important branch of theology as it directly connects to historical theology in its studies and therefore directly impacts practical theology. Biblical theology becomes closely tied with the work carried out in exegesis such that it isn’t uncommon for people to argue biblical theology to be little more than part of exegetical theology (more on this later).