Incenter (I): Point in the interior of the triangle that is equidistant from the three sides. This can be found by determining the angle bisectors of each angle, since the angle bisector is equidistant from the two sides. The incenter will be at the intersection of the angle bisectors.
Incircle: Circle inscribed internal to the triangle. The incenter is the center of the incircle.
If Geometers Sketchpad available: GSP Incircle and Incenter