In general relativity, a geodesic that is perpendicular to itself; that is, its inner product with itself is zero, hence the term null. Obviously, null geodesics are non-existant in Euclidean geometry, but they do exist in physical four-dimensional geometries, that is, ones with signature +/- 2. Photons and other null particles follow null geodesics.

Yet another bizarre and difficult-to-visualise concept in GR.