Upper Manhattan is an area in New York City consisting of the thin, northern neck of the island of Manhattan. While most of Manhattan Island is flanked on the east by the East River, the East River curves away from Manhattan at around the Triborough Bridge; Upper Manhattan could be best described as the part of Manhattan immediately west of the Harlem River as opposed to the more famous part of Manhattan which lies immediately west of the East River. This definition corresponds roughly to Manhattan north of 125th Street, encompassing the northern half of Harlem as well as the entirety of the neighborhoods of Washington Heights and Inwood. In essence, Upper Manhattan is the "panhandle" of the island that visually "fits into" the borough of the Bronx rather than the part sitting across the East River from the boroughs of Brooklyn and Queens.
Upper Manhattan could be described as the "non-tourist" section of Manhattan. Not only do New York tourist maps not normally acknowledge the boroughs of the Bronx, Brooklyn, Queens, and Staten Island, but they also regularly neglect Upper Manhattan as well. This is likely due to the less glitzy, less tourist-friendly, and high-crime nature of the area. Even many native New Yorkers tend to treat Upper Manhattan like an outer borough; its greater distance from Midtown and unusually low rent leads many to exclude this northern neck from the area New Yorkers call "The City".
All of Upper Manhattan is contained in the larger area New Yorkers know as Uptown (above 59th Street.) The Bronx, though not in Manhattan, is often colloquially referred to as "Uptown", especially in hip hop/inner-city culture.