Vertices

A vertex (plural: vertices) is a point where two or more straight lines meet.

It is a Corner.

This tetrahedron has 4 vertices.

And this pentagon has 5 vertices:

Edges

An edge is a line segment that joins two vertices.
This tetrahedron has 6 edges.

And this pentagon has 5 edges:

An edge can also be the boundary of a shape. Such as the circumference of a circle.

Faces

A face is any of the individual surfaces of a solid object. This tetrahedron has 4 faces (there is one face you can't see)