Isometries are transformations the plane which don't distort shapes. For this reason, another common name for an isometry is a rigid motion. The most familiar isometry is probably just translation -- shifting a shape in a straight line. However, another very familiar kind of isometry is rotation:

Unlike translation, this isometry has an obvious fixed point. The pivot point around which everything rotates doesn't move at all. Using the analogy of a square drawn on a large transparent sheet of plastic, you might do a rotation by holding down the pivot point with your finger, and whirling the sheet around it.

Translations have no fixed points at all, while rotations have exactly one -- namely, if you stay away from the pivot point, everything else moves. This is worth pointing out, since it suggests a way of classifying any kind of isometry, by considering their fixed point behavior.