Temple Square is the section of land located at the numeric center of Salt Lake City. It is so called because it is, indeed, a rectangular plot of land (as are the majority of all plots in Salt Lake City proper), and it is where the best-known LDS Temple resides; hence "Temple Square".
This point in the valley was not the first section of land designated as is the general story, but it was one of the first. However, the story goes that when Brigham Young, the leader of the religious faith that the majority of the pioneers held, first entered the valley on July 24th, 1847, while examining the area around the first encampment (at what is now City Creek Park), he stopped and thrust his cane into the ground and declared "This is where the Temple shall be built". The story continues that one person in his group hammered a stake into that exact spot which, much later, would be where the conerstone of the Salt Lake City LDS Temple would be laid.
The property and the contructions therein have had some interesting history, including the foundation being plowed over to avert suspicion when a convoy Soldiers came to report on what the crazy "Mormons" were doing out in the middle of the desert, and later having the entire site torn out and reconstructed early on when it was found that a sandstone foundation was not nearly strong enough and would need to be replaced with granite.
But down to brass tacks. The actual property is flanked on 3 sides by North, South and West Temple Streets; it was also flanked by East Temple, but the section of that road immediately adjacent to the lot was turned into a pedestrian park in 2001. On the three sides that face streets there is a sandstone and plaster (now stucco) wall, though the side that faces the new pedestrian park has been torn down. All street numbers are figured from this point in the form of "100 South", "200 South", etc, radially. That means to the west of Temple Square is West Temple, and west of that is "100 West", and it also means that 300 North and 500 South would run parallel to each other, as would 400 East and 100 West.
In the original block resides not only the LDS Temple, but many other Landmarks of the Pioneer heritage. Among them are two visitors centers, the Assembly Hall, the ever-impressive Salt Lake Tabernacle, the bronze bell from the LDS temple in Nauvoo, Illinois (which was destroyed by mob some years earlier), an 11-foot replica of Thorvaldsen's Christus and an acre or two of walking paths flanked by trees and shrubbery. Now that the block has been extended by removing the above mentioned street, the block as a whole also adds the Joseph Smith Memorial Building (formerly the Hotel Utah) the old LDS Administrative Building and the Church Office Building, the tallest building in the valley (by number of stories; by height it is the second).
Excepting the Temple itself, Temple Square is probably best known in the area for its Christmas light displays. Every year on the day after Thanksgiving, light are put on and around every tree and hedge on the ground; yearly figures vary, but on average 100,000 mini-lights are used in the grounds. The lights are usually taken down soon after January 1st, but it seems that the lights are being left up for the enjoyment of the crowds that will be on hand for the 2002 Winter Olympics.
The grounds are open to the general public from 9AM to 9PM daily. There is no admission charge and tours are given free in 40 languages thanks to the Church Service Missionaries on hand.