To describe a circle with any center and radius.

Circles were defined in Def.I.15 and Def.I.16 as plane
figures with the property that there is a certain point, called the The given data are (1) a point |

Note that this postulate does not allow for the compass to be moved. The usual way that a compass is used is that is is opened to a given width, then the pivot is placed on the drawing surface, then a circle is drawn as the compass is rotated around the pivot. But this postulate does not allow for transferring distances. It is as if the compass collapses as soon as it’s removed from the plane. Proposition I.3, however, gives a construction for transferring distances. Therefore, the same constructions that can be made with a regular compass can also be made with Euclid’s collapsing compass.