A covert listening device, more commonly known as a bug or a wire, is usually a combination of a miniature radio transmitter with a microphone. The use of bugs, called bugging, is a common technique in surveillance, espionage and in police investigations.
A bug does not have to be a device specifically designed for the purpose of eavesdropping. For instance, with the right equipment, it is possible to remotely activate the microphone of cellular phones, even when a call is not being made, to listen to conversations in the vicinity of the phone.
A "wire" is a device that is hidden or concealed under a person's clothes for the purpose of covertly listening to conversations in close proximity to the person wearing the "wire". Wires are typically used in police sting operations in order to gather information about suspects.
The act of "wearing a wire" refers to a person knowingly recording the conversation or transmitting the contents of a conversation to a police listening post. Usually it's accomplished by some sort of device that is attached to the body in an inconspicuous way, such as taping a microphone wire to their chest. "Wearing a wire" by undercover agents is typical plot element in gangster and police related movies and television shows. A stereotypical move scene is when someone is suspected of "wearing a wire", the criminals will tear the suspect's shirt open hoping to reveal the deception.