
A cross section is the intersection of a figure in threedimensional space with a plane. A cross section is the face you obtain by making a "slice" through a solid object. A cross section is twodimensional. 

We see cross sections in everyday life.
A "slice" of bread.
Cross section:

A "slice" of cucumber.
Cross section:

A "slice" of log.
Cross section:

When a plane intersects a solid figure, the cross sectional face may be a point, a line segment, or a twodimensional shape such as, but not limited to, a circle, rectangle, oval, or hexagon.
Point
The plane is tangent to the sphere, intersecting in only one point.

Line Segment
The plane is tangent to the side of the cylinder, intersecting in a line segment. 
Figure
The plane cuts through the figure, intersecting in a pentagon. The plane may, or may not, be parallel to the base of the figure.

The figure (face) obtained from a cross section depends upon
the orientation (angle) of the plane doing the cutting.
Right circular cylinder
Cross section: rectangle
Plane orientation: perpendicular to the bases 
Right circular cone
Cross section: ellipse
Plane orientation: slanted (angled) across the cone 
Right square prism
Cross section:
square
Plane orientation: parallel to the bases of the prism 
A single solid figure can be sliced to produce numerous cross sections of different forms.
In the diagrams below, the sword represents the "slicing" plane.
The solid object is a right rectangular prism.