An edge is a line segment connecting two vertices. An edge always connects two vertices by a straight line. The edges are the “wires” you see when you look at a mesh in wireframe view. They are usually invisible on the rendered image. They are used to construct faces.

Edges are used extensively in blender. Every mesh is represented with vertices edges and faces.

Documentation for many edge editing tools on the Blender Manual.
Wikipedia article on geometric edges.