Manhattan is the most densely populated borough of the five boroughs that comprise New York City, and the one referred to as "The City". Manhattan is the financial, cultural, media, and entertainment capital of the world. Ask any New Yorker and they will assure you Manhattan is the center of the universe.
Manhattan is divided down the center by Central Park, each side demarcated as the East Side or the West Side. It is a
city of neighborhoods, from Yorkville to SoHo to the East and the West Village and from Uptown to Midtown to Downtown. Neighborhoods are identified by geography and nickname: TriBeCa is the Triangle Below Canal Street, SoHo stands for South of Houston Street, as NoHo stands for North of Houston and NoLIta is North of Little Italy.
Manhattan is laid out as a grid except for Greenwich Village and the streets go north to south and the avenues go east to west. Subways and buses crisscross the entire borough but it's best to walk the cobblestone streets of Lower Downtown and the avenues of Midtown to get the true flavor of Manhattan.
And to make sure you don't miss anything the city has to offer; check out NY2C for food, shopping, entertainment, and more.