Something intrusive is getting in your face or invading your space. Nosey questions, a poke in the ribs, and a hovering mother are all intrusive.
Things that are intrusive are a real pain in the neck: they intrude on you. If someone asks you a million questions, especially personal questions, that's intrusive behavior. When photographers hound celebrities, they're being intrusive. If a rock is sticking out and getting in people's way, then it's intrusive. All meanings of intrusive involve something being where it doesn't belong.