A nick is a tiny cut or scratch. Your neighbor might be so proud and protective of his brand new car that even a nick in its paint would be deeply upsetting to him.
To make a nick is also to nick: you might accidentally nick your dog when you're cutting tangles and mats out of her fur, or nick yourself when you're gathering up pieces of a broken glass in the sink. Informally, you also nick someone when you cheat them out of some cash or nick something when you steal it. If help arrives "in the nick of time," it comes at the very last possible second.