If something is bugged, it has a secret microphone or camera planted in it for spying on people. A TV detective might say, "Don't say anything! The room is bugged."
A bugged phone has a small microphone hidden inside it so that some person or organization can listen in on its owner's conversations. If your computer is bugged, a spy can see every link you click on and each email you send. This meaning of bugged has been used since the early 20th century — a so-called bug, or surveillance system, is named for its tiny, bug-like size.