To be mad at someone means your upset with the person or thing, and you don't want to have nothing to do with it anymore or for a couple minutes or hours.
Example: The big bang theory, Season 8, Episode 15:
Penny: What's going on?
Sheldon: I'm mad at Amy.
Penny: Did she leave pit stains in your favourite crop top, too?
Sheldon: No. She helped Barry Kripke make an advancement in string theory.
Penny: Oh, that sounds like a good thing.
Example: The big bang theory, Season 8, Episode 15:
Penny: What's going on?
Sheldon: I'm mad at Amy.
Penny: Did she leave pit stains in your favourite crop top, too?
Sheldon: No. She helped Barry Kripke make an advancement in string theory.
Penny: Oh, that sounds like a good thing.