This is a polite, formal way to talk about something that you have to do, or to ask for something. People in customer service jobs often speak this way.
Here are some examples:
I'll need to check your I.D., sir.
I'll need to check with my manager. Please hold a moment.
You can also say "I'll need you to ____":
I'll need you to verify your address, please.
I'll need you to sign right here.
When you're not speaking as politely or formally, you can drop "will":
I need to see your I.D.