Tesla was an engineering giant but it is true that in most cases, he was just a crackpot when it came to theoretical physics. This "theory of gravity" is one of the major ones.
It wasn't really connected with gravity - the attraction of objects to the Earth etc. with a universal acceleration - by anything else than a wishful thinking. As expected for the practical guy, most of the support for his unusual claims came from experiments, and it was the electromagnetic experiments.
Tesla claimed that the vacuum was filled with a new kind of the aether, a rarified gas that he also called the Akasha. This name is relatively important in his theory so you can get some idea about the character of the theory. The Akasha was extremely elastic.
Some spectacular experiments with some light emitted by either dielectric materials or conductors were made to support the claims, although they didn't have anything to do with the claims about the unifying theory. And at the end, it was found out that the experiments analyzed solidified air rather than any mysterious matter that could be filling the vacuum.
So the theory was a complete nonsense. Tesla couldn't really distinguish the fundamental phenomena from the highly derived, environment-dependent ones.