Cross-section:  The region formed by the intersection of a solid and a plane.
Cross Section

Below are three cross sections of a pyramid with a square base:

If the pyramid is cut with a plane (green) parallel to the base, the intersection of the pyramid and the plane is a square cross section (red).
If the pyramid is cut with a plane (green) passing through the top vertex and perpendicular to the base, the intersection of the pyramid and the plane is a triangular cross section (red).