Nasty = unpleasant (opposite - nice)

* David is very nice. He's warm and friendly. But his brother is a nasty character. He's rude and unpleasant.

** There's a nasty smell in here.

*** He had a nasty cut ( = deep/painful) above the eye.

**** What do you expect? It was a cheap and nasty ( = inexpensive and bad quality) watch. No wonder it's broken.