Use this expression when you're angry about someone's behavior. You think that there's a basic standard, but this person didn't meet that standard. For example:
He didn't even call you on your birthday? What a jerk!
In this example, you actually think that this person should have done more than call. He should have sent a gift or taken this person out for dinner.
Here are some more examples:
They didn't even offer to help me.
It took over an hour for them to bring us our food, and they didn't even apologize!