Originally named after Union rallies held during the Civil War, Union Square became the fashion center of San Francisco and still hosts many of the city's most prestigious stores (Barneys, Saks, Neiman, etc), with others just a few blocks down Powell street at the San Francisco Centre.
Built during WW2, the world's first parking garage (welcome to California!) sits underneath the square and was designed to double up as a bomb shelter, but BART and Muni are often faster and cheaper :)
Union Square adjoins the overlapping Gallery and Theater districts. Otherwise, Mark Hopkins or Harry Denton's Starlight Room offer panoramic views and libations. At night, Ruby Skye and Slide are often busy. Aforementioned Starlight Room can be quite a meat market on hump day's night (Wednesday).
During the holiday season an outdoor ice skating rink is erected in the square itself (along with another at Vallaincourt Fountain).
Wikipedia: http://en.wikipedia.org/wiki/Union_Square,_San_Francisco,_California