If you take a solid and slice it, then the face you create is called a cross-section and the area of the face is called the cross-sectional area. Definition: A prism is a solid with straight sides which has the same cross-sections, where the cross-sections are all parallel to a face.
In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross sections.
Cross section area is an area of an object if you view it as a 2D object. For example, imagine a perfectly rounded ball. If you look at the ball and view it as 2D object, you will see a circle with radius equal with the ball. Another example , imagine a cone. If you look at the cone from the top, you will see a circle. That is the cone cross section viewed from top. If you look the cone from the side, you will see triangle. That is cross section of the cone viewed from the side.