Projective Geometry is a geometry that is different from the usual Euclidean Geometry students learn in high school. In Plane Euclidean Geometry, two points determine a line and each two lines either intersect in a point or are parallel. Given a line and a point not on the line there is exactly one line parallel through the point. In Plane Projective Geometry, two points determine a line and each two lines intersect in a point. A finite Projective Plane is a Plane Projective Geometry with a finite number of points and lines. The one that appears on the T-shirt has 13 points and 13 lines. There are several spots that look like lines cross, but they do not. The only intersections are at the numbered bold points. The other crossings are only there because the schematic picture was drawn on an ordinary plane.

More information about projective planes may be found e.g. at

http://en.wikipedia.org/wiki/Projective_plane

For a fascinating story please see The Search for a Finite Projective Plane of Order 10

This can also be read in the American Mathematical Monthly volume 98, 1991, pages 305 - 318.