If you have a modern digital phone, the answer is very complicated. So I'll describe the old-fashioned analog phones, like standard landlines.
The sound you hear is a pressure wave in air. That means that the air pressure oscillates back and forth, pushing your eardrum in and out, triggering nerve signals. The phone lines carry an electrical current that runs back and forth following the same pattern in time as the air pressure.
The current is made by a microphone, which uses a diaphragm that's pushed back and forth by the sound waves to make a back-and forth electrical current. There are several different ways those microphones can do this. The current is sent through electrical wires to the other phone. In order to keep the current strong enough, some amplifiers are used, which pump energy into the current without changing its back-and-forth shape. That current drives a diaphragm in the earpiece back and forth, pushing on air to make a sound pressure wave that sounds the same as the the sound spoken into the first phone.
The wikipedia article on telephones is quite informative:
(published on 06/01/09)