Space exists around things with mass. Also, above-absolute-zero temperatures cause particles to jump around randomly.
Now if there is "more space" around particle A, particle B will have a slightly higher statistical chance of randomly jumping closer to it, than farther.
Now if there is "more space" around particle A, particle B will have a slightly higher statistical chance of randomly jumping closer to it, than farther.
Rinse-repeat. Gravity as we know it.