“Let me tell you a bit about my background.”

You are giving a presentation at a conference. You are at the beginning of the presentation. You've said your name and thanked the person who introduced you. Now you want to tell the audience about yourself. You start by saying:

Let me tell you a bit about my background.

Let me (do something)

You say "Let me ___" when you are announcing what you're going do do:

Let me give you a few examples.

This is similar to "I'd like to ___" but "Let me ___" sounds a little more confident.

a bit

"A bit" is a small amount. Saying "a bit" sounds more sophisticated and intelligent than "a little".

(someone's) background

A person's "background" is their personal history. "Background" is the part of the history of something that you need to know in order to understand a situation. So for a person giving a presentation at a professional conference, the "background" is information about what he studied in school, where he worked, and so on.