What describes the point where three angle bisectors of a triangle meet?

Answer 1

The point where all three angle bisectors meet is the centre of the incircle - the circle which touches all the sides of the triangle (alternatively described as the circle for which the sides of the triangle are tangents).

Answer 2

The answer is nearly in the question! One way to describe it is : it is the meeting point of the three angle bisectors of a triangle.