Exegesis is the process of attempting to interpret a text, which could be a matter of explaining it in terms familiar to readers from a context other than the author's (which can approach or include translation), offering a critical examination, or extrapolating statements in the text to discover implicit information. It means "to lead out", that is, to make the implicit explicit. There is a long history in literate cultures of textual exegesis, building on a sacred or revered text by providing interpretation and critique. The Torah, New Testament, Vedas, LaoZi, Confucius, Qrān, and numerous other authors and books have an extensive body of exegesis around them.
Eisegesis is more or less the opposite or complement. It's what happens when an author uses a text to prove a predetermined thesis drawn from outside the text, "reading into".
In theory the two are separate, but our Monkey OS instincts are not so good at differentiating. Honest scholars work hard to do the former and avoid the latter, but inevitably, we see what we are prepared to see.