A center is a point that is the same distance from all the extremities of a figure.
The center of a circle is the point which is equidistant from all points on the circle. In the figure below, C is the center. The center point is often used to label the whole circle. The figure below would be called "the circle C".For more on this see Circle definition.
The center of a regular polygon is the point that is same distance from all its vertices.For more on this see Center of a regular polygon.