The term "base" can be used in a number of different mathematical contexts:
base of a plane figure
The base of a plane figure is usually thought of as a side on which the figure "sits." In the figure below, the red line indicates one base of the plane figure:
base of a space figure
A base of space, or solid, figure is usually thought of as a face upon which it can "sit." In the figure below, the red face indicates one base of the space figures:
Note that in most cases, figures, whether plane or space figures, have more than one base.
The term "base" can also be used in the context of numeration systems and exponents.