When you emend a piece of writing, you correct or revise it. If you are asked to emend a report, that just means you need to go through it and make revisions.
Emend is similar in spelling and pronunciation to another word, amend, and there’s a slight overlap in meaning as well. Emend refers to changes and improvements made to a text. Amend also can refer to making minor changes to a text, but it can be used to describe improvements made to other things as well — for example, you can amend a situation. In contrast, emend’s powers are limited to words. So if you’re using emend — the one with the "e" — just make sure you’re describing improvements that involve text.