This is a simple question, but the answer could make several pages. If you take Einstein's hypothesis. Mass (the "cause" of gravity) bends space (or more accurately "spacetime"). The act of "falling" is merely travelling along "straight" paths in a space that is fundamentally curved. (Take a look at the "equivalence principle" - there's a good wiki page.) This is the relativistic model.
Planck and other "quantum people" hypothesise that gravity is caused by the exchange of subatomic particles (gravitons). This is part of quantum theory.
Newton just assumed that the force exists, rather like magnetism, he explained how it worked (so well, in fact that it approximates VERY closely to the relativistic model, despite being fundamentally flawed). He didn't bother to try to explain what it was.
We know that the first two theories cannot really co-exist, although some, like Steven Hawking are trying to combine them in the "Grand Unified Theory".