How was gravity explained in Ancient Greek and Roman times?
As xxavier and Mauro say, people like Aristotle claimed that things had a natural affinity or tendency towards a certain location. That's no explanation at all. That's what's missing from the Wikipedia article sempaiscuba was referring to.
The Wikipedia article does include a section on general relativity which purports to explain gravity. However it doesn't. Note this: "Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime". He didn't, because:
Spacetime curvature is associated with the tidal force, not the force of gravity.
Spacetime models space at all times, so there's no motion through spacetime.
A concentration of energy causes spacetime curvature not just matter.
What Einstein did say is this: “As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable”. Unfortunately you tend not to hear about this, which means gravity is generally not explained in modern times either.
Gravity is of course something that we can all observe. Stuff falls towards the ground. But not everything: some things like steam or smoke defy this force and instead float up.
However they don't do this in a vacuum. Note that the Wikipedia vacuum article says this: "Vacuum has been a frequent topic of philosophical debate since ancient Greek times, but was not studied empirically until the 17th century". The ancient Greeks weren't big on experiment.