One of the first theories to describe what causes gravity is general relativity, proposed by Einstein in 1915. In this theory, space (ie. our three dimensional world) and time are objects, and matter interacts with spacetime changing the shape of it. A two dimensional model can be thought of as a ball on a soft surface. Placing the ball on the surface will make the surface "sag" since the weight of the ball pushes into the surface. If the ball is light, the surface hardly deforms. But if the ball is very heavy, then the surface will cave in, much like the picture below:
If we take the picture above as an example and place a marble near the edge, that marble will slowly be pulled into the pit since that is what the curvature dictates.
Now suppose we couldn't see the surface. We would observe the marble, somehow, moving on its own towards the heavier ball. This was how Einstein explained gravity through general relativity. He thought that heavier masses (like the Sun) deformed spacetime and that this deformity interacts with other matter (like the Earth) to produce this effect of "gravity".
General relativity is quite effective and explained many scientific questions about how large massive objects interact. Furthermore, the theory has been tested and validated in many ways. For instance, the GPS relies on time dilation effects that are the result of relativity. Gravitational lensing was another validation.
However, the incompatibility of general relativity with quantum mechanics led to the development of a new theory of gravity... quantum gravity. Stay tuned for the next post!