Sarky is informal British (and also Australian) English for sarcastic. If someone is being sarky, they are making sharp, mocking remarks — the kind that pretend to be polite but are not. You hear it in speech: “Don’t get sarky with me.” It is a bit cheeky as a word; people use it when they want a short, ordinary word instead of sarcastic. American English almost never uses it. It has nothing to do with the island Sark, even though the spelling looks close.