The trailing edge of a wing or airfoil is the (usually sharp) part furthest downstream in the fluid flow. Under low speed conditions, that is, a freestream velocity of less than 100 m/s, the flow past the trailing edge obeys the Kutta condition that the flow must converge to leave the trailing edge smoothly. However, as angle of attack increases (as a rule of thumb, to more than about 10°), the flow can no longer make the large change in momentum and separates, creating turbulence and causing the wing to stall.
On a finite wing, the trailing edge is home to the trailing edge vortex, which induces a downward change in momentum. The Prandtl lifting line theory uses the concept of trailing edge vortices to analyze the performance of a wing.
The trailing edge of a real, working airplane wing is where you'll find a variety of control and high lift system gadgets, including (but not limited to) flaps (split or trailing), ailerons, spoilers, and clever combinations such as flaperons. When sitting in an airliner, these are the things you are most likely to see working—as opposed to the elevator, which is at the trailing edge of the horizontal stabilizer, and the rudder, at the trailing edge of the vertical stabilizer. Trim tabs can also be found on the trailing edges of these aft-mounted "wings".
Not to be confused with the leading edge, which is upstream.