Manhattan Island is a long, narrow island. As most everyone knows, its streets are laid out mostly in a grid pattern, with avenues running uptown/downtown (North/South, roughly) and streets running across town (east to west, roughly). (I say 'roughly' because Manhattan is actually canted Northeast to Southwest, but nevermind.) So as to make things easier, avenues are numbered from East to West, and streets are numbered from the southern tip northwards. Sure, this system is highly eccentric, what with streets not running straight and sometimes predating City Planning, but you can generally assume that a higher-numbered street is uptown of a lower-numbered one, and a higher-numbered avenue is west of a lower-numbered one.
Around 14th street, however, the east side of the Island bulges out a bit, interrupting the East River shoreline which is fairly straight uptown of 14th. As a result, First Avenue below 14th street is inconveniently far inland, and four 'short avenues' between it and the East River appear. Since it would just be confusing to name these with negative numbers, they are instead lettered, with Avenue A just East of First and so on up to Avenue D.
So, from 14th street on the north to East Houston street on the south, and Avenue A on the west (some say First avenue is really the boundary), to Avenue D on the east is a roughly quadrilateral area which is referred to as 'Alphabet City.' Tompkins Square Park is found there, midway between the north and south ends along the western edge. There are no subway stops in Alphabet unless you count the L train stop on 14th and First Ave, although buses cross it. Just north of Alphabet, across 14th street, is the famous (or infamous) Stuyvesant Town development.
Traditionally an immigrant neighborhood, Alphabet has traditionally been home to tenements, walk-ups, seedy bars and generally low rents. Although the ethnic groups inhabiting it have changed many times, it's still known as a place where someone with not a lot of money (for New York) can get a flop. It achieved some fame in the literary world with the rise of the beat poets, as Allen Ginsberg spent nearly all of his adult life living within the boundaries of Alphabet. Fritz the Cat began his odyssey of counterculture freakout in Tompkins Square Park, IIRC. Ginsburg and Jack Kerouac took a walk around Alphabet in 1953 (I think) and Ginsberg took several pictures of Kerouc in front of recognizable landmarks which have since become famous.
Along with its immigrant and generally impoverished character, Alphabet has been associated with a high crime rate. The large number of bars in the area didn't help. The local Hell's Angels have their clubhouse in the area, and the 1960s drug culture never really left before morphing into the harder and darker crack-fueled chaos of the 1980s.
Starting in the early 1990s, Alphabet began to succumb to the wave of gentrification that was sweeping New York City. As of 2011, it's still got a distinctive feel, but it's much safer than it used to be, rents are higher, and many New Yorkers would tell you bitterly that it's just become damn boring and out of reach of the more interesting folks who used to live there. This is certainly true; while once it was an artist's community, now you'll find The One Percent wandering around looking for likely-looking older buildings to redevelop into incredibly expensive condominium lofts and luxury apartments.