Updates inform you about new followers, new publications of yours added by your co-authors, comments on your publications, answers to questions you asked or followed, and much more. Clicking on the update takes you directly to the new content, so you can instantly see who is interacting with your research and how.
Messages are where you can find private messages either sent to you or sent by you.
Requests contains all Feedback, Full-text, Author, Skills and other types of requests. These generally require some kind of answer or confirmation.