Euler Circuit 

The squares in this figure were traversed without going over the same path twice.

Leonard Euler discovered that a figure can be traced only if it has 0 or 2 odd vertices. An odd vertice is the number of lines that meet at a point. Looking at the 14 vertices in this figure, four vertices have 2 lines meeting and twelve vertices have 4 lines which meet. This figure therefore has 0 odd vertices.

If a figure has 0 odd vertices, the start and finish are the same point which is the case here.

If a figure has 2 odd vertices, the start and finish are at different points.

A Euler Path traverse every line exactly once.
A Euler Circuit is a Euler Path which starts and ends at the same vertice.