Eavesdropping means to listen to things you aren't supposed to hear. It is a deliberate act, rather than simply overhearing someone else talking. Police and security forces are eavesdropping when they put a tap on to a person's telephone line to listen to the person's calls. Intelligence and security agencies are eavesdropping when they put an electronic listening device, a bug, into a room.
Governments and the military have also built large facilities designed to listen in to communications between other governments and military groups. For example the US has a large base at Pine Gap near Alice Springs, Australia, which listens to communication signals from all over the world.