The Triforce is the great Golden Power that binds Zelda, Link and Ganondorf together. According to legend, the 3 Godesses left it in Hyrule when they went back to the heavens. It has three powers; Wisdom (the gift of Nayru, and controlled by Zelda), Power (The gift of Din, and controlled by Ganondorf), and Courage (The gift of Farore, and controlled by Link).

 

The completed Triforce has the power to grant the deepest desires and wishes of whoever controls it, and near-unstoppable power. It is influenced by the heart of the one weilding it; it can be used for great good or great evil.

 

The Triforce can be split into its 3 individual parts. Those parts can be further split into groups of 8 peices (such as in Wind Waker when the Triforce of Courage is split into 8.

 

In-Game:

The Triforce was rumored to be an item in Ocarina of Time after screeenshots showing Link pulling it out of a treasure chest were released by Nintendo. However, it was not included in the final game (although it is apparently part of the coding). It is not possible to obtain the full Triforce in any game in any way.

 

In certain games you can collect split up Triforce peices. In the original Legend of Zelda, you have to collect peices of the Triforce of Wisdom. In Wind Waker you must find the peices of the Triforce of Courage. 

 

In some games, such as Oracles of Ages, Oracle of Seasons,  and A Link To The Past, the Triforce is a living object. In others it is shown as inanimate but omnipotent (giving its users ultimate power).