Haight Ashbury is the intersection of Haight Street and Ashbury Street, and is generally thought to be the birthplace and gathering spot for the 1960's cultural revolution. On the corner are a Ben and Jerry's scoop shop, Haight Ashbury T-Shirts, and the vintage clothing shop Aardvark. There used to be a Gap, but it closed down. The smallish yet famous area is home to many vintage and second-hand clothing shops as well as cafes, smoke shops, and the illustrious Amoeba Records. You will often find many tourists in this area looking for a piece of the summer of love!
The neighborhoood, colloquially known as "the Haight," is divided into the Upper Haight, toward Golden Gate Park to the west, and the Lower Haight, also known as Haight-Fillmore, which extends closer to Market Street to the east. Haight and Ashbury intersect in the Upper Haight. The Lower Haight area isn't considered a particularly safe neighborhood, and many people cite the nearby housing projects as the source.
The region is surrounded by Golden Gate Park and the Sunset to the west, Cole Valley to the south, Hayes Valley to the east, and the Western Addition, NoPa and Alamo Square neighborhoods to the north.
You can read all about that on Wikipedia for the most part, but maybe you'd be interested in seeing this KPIX documentary that shows Haight-Ashbury in 1967 (surprise: it kind of looked normal).