Osculating circle
In differential geometry, the osculating circle of a curve at a point shares a common tangent line and a common radius of curvature with the curve at that point. Osculate literally means to kiss.
In "laymen's terms"
Imagine driving a car along a curved track on a vast flat plain (or "plane", in mathematicians' language). The car can freely move rather than staying on the path. Suddenly lock the steering wheel in its present position at one point along the path. Thereafter, the cars moves in a circle. The curvature of that circle is equal to that of the road at the point at which the steering wheel became immovable. That circle is the osculating circle of the curve of the road at that point.