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.