A graph homomorphism between two finite graphs F and G is an adjacency preserving map from the vertex set of F to the vertex set of G. Many important properties of graphs can be expressed in terms of graph homomorphisms. For instance, F is 4-colorable if and only if there is a homomorphism from F into the complete graph on four nodes. Let hom(F,G) denote the number of homomorphisms from F to G. For G fixed, hom(--,G) is a graph parameter on finite graphs. Freedman, Lovasz and Schrijver have recently characterized those graph parameters that are of the form hom(--,G) for a fixed G. The proof involves a surprising connection to finite dimensional algebras and their idempotents. I will attempt to give an expository talk on this result which is part of a very large body of recent work on this topic due to many people including Freedman, Lovasz, Schrijver, Borgs, Chayes, Sos, Szegedy, Vesztergombi and others.