The circumcenter of a triangle is the point where the three perpendicular bisectors of a triangle meet. It is also the center of the circumcircle (the circle that goes through the vertices of the triangle). Sometimes the circumcenter is outside of the triangle, itself.
Think about what that means: What do you know about circles? What is the center of a circle? The center of a circle is equidistant to all points on the circle. This means that the circumcenter is equidistant to all of the vertices of the triangle since the circumcircle touches all three vertices.
