What is known is that the space between Galexies is expanding. Gravity is strong enough to hold the galexy groups, galexies, stars, solar systems, and planets together, but in between galexy groups there is not enough gravity to counterbalance the expansion of space. Edward Hubble discovered this in the 1920's. He started cataloging the distance a galexy was from us, and its speed. He found that all non-local galexies were moving away from our Galexy, and the further the galexy was from us, the faster it's speed. The only way to explain this is that space is expanding. In the late 1990's a further investigation of really distant galexies showed that the expansion rate decreased the further (and therefore older) the galexy was from us. If you think about this that means that the expansion rate has been increasing. This expansion is a good thing, because without it our Universe would have fallen in on itself long ago.
Now if you are asking what is fueling this expansion, and the increasing expansion rate too, there is no good theory. The energy necessary to fuel the expansion increase aocounts for 73% of the mass-energy in our universe, so it is not a trivial amount, and Physisits call this "Dark Energy", but are clueless about its origin.
I hope this helps...