“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 this.
Let me tell you a bit about my background.
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Let me (do something)
When you see or hear the words "Let me...", you may think that the speaker is asking for permission, but that's not true. This phrase is used in both casual and formal situations to announce what you're going to do:
Let me give you a few examples.
This is more confident-sounding than "I'd like to ___". It's more polite than "I'm going to ___."
"A bit" is a small amount. Saying "a bit" sounds more sophisticated and intelligent than "a little".
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.