My understanding of induced drag,
Due to the pressure differential above and below the wing the wing suffers from a spanwise flow of air. Air beneath the wing flows out and air above flows inwards. Where these airflows meet again at the trailing edge and most significantly at the wing tip, vortices are generated. The bigger the pressure differential (aka lift generated) the greater the vortices. These vortices induce a downwash to the airflow behind the wing. The downwash has a net effect on the relative airflow of giving it a vertical componant and as a result the effective airflow is now no longer parallel to the aircraft flightpath but is angled down as you look at a cross section of the wing from leading edge to trailing edge. The lift generated is perpendicular to the effective airflow and therefore has a rearward component compared to the direction of travel of the aircraft. This rearward component of the lift vector is the induced drag.
Bit wordy, but a brief definition would be the rearward component of the lift vector. If I've got it right.
