After the course of the Immortal War, the Gods were unable to have any real affect on the world. The result was that many Gods were inclined to give their power to sentient beings on Jove, thus allowing the bearer of the Gift/Curse to be able to control/be influenced by the same Aspect as the God. For example, the Champion of the God of Cause and Effect, the Blood Princess, can control Cause and Effect, allowing her to cause without effect and generate an effect without cause. She can therefore do almost anything, but her abilities change her and cause her to be reliant on them. This can cause further problems, for example when she ends up in the Land of Trees and is unable to use these abilities.
Not all Gods had influence over the world in physical ways, and some Champions manifest the influence of the God in different ways. The Champion of the God of Truth constructs sculptures of himself that line the equator of the planet, but has no ability to stop them being destroyed or to anything extraordinary (besides being a prolific artist).
Champions are created, usually by accident, when a champion-less God comes into contact with a non-God sentient being.