Pace asterphage, the qibla is specifically the direction of the Kaaba. That's at 21° 25' 24" N, 39° 49' 24" E, if you're into blasphemous geocaching.
Since the earth is a sphere (more or less), determining the qibla is more than just a matter of drawing a line on a map. On that map, for example, the direction from my apartment, in a heavily Pakistani neighborhood in Brooklyn, to Makkah would appear to be southeast.
The qibla, however, is the shortest distance on a Great Circle arc. If I were to convert to Islam, I'd actually have to pray facing northeast*. The exact direction is calculated using spherical trigonometry -- at my apartment it's roughly 58 degrees from true north.
*It's for similar reasons that the flight paths on the maps in airplane magazines are arcs rather than straight lines: on a globe, those are straight lines.
Source: http://www.salon.com/tech/col/smith/2003/03/07/askthepilot31/