Perhaps the wikipedia article was a bad link, because it talks about things from the algebraic perspective. Algebraic operations are equivalent to general-purpose programs if you are willing to let things run more slowly; it turns out that computers are built out of ANDs and ORs, which is exactly what homomorphic encryption lets you do. For C programs the slowdown is significant. For logic circuits the slowdown isn't very significant. For LISP programs the slowdown is intermediate.