Mirror of Twilight

In Twilight Princess, the Mirror of Twilight was the link between Hyrule and the Twilight Realm. Made by the gods, the mirror allowed people to travel in between the two interlinked worlds as pleased. Located in the desert, the Twilight Mirror was used to banish and imprison the most evil of criminals of the kingdom into the Twilight Realm, never to be seen again.

Location and Background
The location of the Mirror of Twilight was well known by most of Hyrule, but many believed it was just a myth. When Link reached its resting ground, the Arbiter's Grounds, he was forced to fight a massive beast, the huge Stallord, in order to reach what remained of the Mirror of Twilight. The Mirror is found within the Mirror Chamber, and is composed of two parts: It is then revealed by the sages that Zant used his newly acquired powers from Ganondorf to break the mirror into four shards, but didn't have enough power to shatter it completely (which Midna succeeds in doing at the very end of the game). Link and Midna must then find all of the shards to complete the Mirror of Twilight and transport them to the Palace of Twilight.
 * The Mirror itself, which acts as a kind of 'projector' which activates the portal.
 * The black stone where the portal forms. The Mirror shines onto this enormous stone slab, creating the portal to the Twilight Realm. It was this very slab of rock to which Ganondorf was chained when the Sages attempted to execute him.

Despite the fact that the mirror is utterly destroyed by Midna, there may be other ways of traveling between the two worlds as Midna mentions many times that she and Link may meet again. Evidence supporting the idea of other methods of travel between worlds is plentiful, the most obvious piece being that Zant is able to travel between worlds without the benefit of the Mirror. There is fan speculation that the Triforce is somehow related to travel between the worlds, as Zant's power was borrowed from the Triforce of Power. Also, only those characters bearing one of the Triforce could reside in the Twilight Realm without becoming a spirit.

Mirror Shard
A Mirror Shard is a piece of the Mirror of Twilight, which Zant broke so that Link could not reach the Twilight Realm. There are four of them for Link to find. One piece is located in the Mirror Chamber where he first learns of this predicament. One is "in the mountains", which is where the Snowpeak Ruins are; another is in a "ancient grove" which is actually the Temple of Time in the Sacred Grove. The last shard is "in the heavens" which is really the City in the Sky. Link must retrieve all three missing shards and head back to the Mirror Chamber to reassemble it. When the Mirror is repaired, Link is able to enter the Twilight Realm and confront Zant.

Similarity to the Dark Mirror
The Mirror of Twilight is believed by some to be the same as the Dark Mirror of Four Swords Adventures. Both are said to be cursed, both are said to possess dark powers, and both sealed away an evil group in the past. The Mirror of Twilight sealed away the interlopers, and the Dark Mirror sealed away a "dark tribe", which may be the Twili. In Four Swords Adventures, the Dark Mirror was hidden in the forest to sever its connection to the rest of the world. In a similar fashion in Twilight Princess, the Mirror of Twilight was hidden away in the desert to separate it from the rest of the world.

However, the two mirrors have different resting places. The Sages guarded the Mirror of Twilight since ancient times at Arbiter's Grounds, and the Dark Mirror was sealed away in the the Temple of Darkness, not Arbiter's Grounds. The Dark Mirror also displays properties not seen in the Mirror of Twilight as well, such as the ability to create Shadow Links.

Trivia

 * When the Mirror is first activated, it broadcasts strange shapes and the symbol of the Triforce. At the opening of Link's Crossbow Training, similar shapes appear and twirl around.
 * In Kirby & the Amazing Mirror, Kirby had to assemble a mirror to defeat Dark Mind, much like how Link had to assemble the Mirror of Twilight to defeat Zant.