A base is one side of a polygon, usually used as a reference side for other measurements. Most often used with triangles.
In the case of a triangle, a common way to calculate its area is 'half of base times height' where the 'height' is the altitude, or the perpendicular distance from the base to the opposite vertex.
For more on this see Triangle definition, and Area of a triangle
If a quadrilateral has a pair of parallel sides, both of them are called a base. And just like triangles, the altitude of such a figure is the perpendicular distance from a base to the opposite side. You can pick either base as your starting point. For example, in a parallelogram:
One or two faces of a solid are sometimes called a base. For example a pyramid has one base, and a cylinder has two parallel bases: