If you know what a nettle is—that is, a barbed seed that gets stuck in your clothes and hair—then you'll have no trouble remembering the verb nettle: it means to annoy, bother, irritate, or bedevil.
A kid sister, a mosquito, an angry boyfriend, or a hot, muggy day: all of these are examples of things that might nettle a person. When you nettle someone, you act like a nettle; you annoy, bother, and generally tick off a person. The person who nettles you can be called nettlesome, which means that they're acting like a nettle. I find that the very sound of his voice nettles me. The sound alone makes me wish he would just shut up.