Newton's Principia of 1687 proposed a mathematical equation that returned the force between two objects, depending only on their mass and distance apart. The gravitational constant G is simply a scale factor to account for the units in use at the time. Newton did NOT describe what gravity was, how fast it propagated or if there was a smallest possible amount, he merely proposed a useful formula. This formula is still useful today, and is the basis of most space travel

Einstein's general relativity, published in 1915, was the first scientific paper to actually describe what gravity was. It is described as a bending of spacetime caused by mass/energy. His equation explained the small deviation from Newton's predictions, seen in extreme or very precisely measured situations. They also predicted truly extreme things, like the existence of black holes

Many of today's physicists don't believe that general relativity completely describes what gravity IS. General relativity is a classical, continuous theory. Our best knowledge of physics is that everything is made of quantum wavefunctions. No one has yet quantized gravity. Some believe that gravity and spacetime are both emergent properties of an underlying quantum reality

Short answer. We still don't know exactly what gravity is

The concept of "gravity" predated Newton, though it sometimes meant different things. The word just means "heaviness" and was used by many people in different ways to explain the observable phenomena that certain things fall to Earth (and others do not) — Aristotle believed this was explained by each substance having a "natural place" that it was returning to (so things made of "earth" wanted to be at the very bottom, while things made of "water" would sit on top of that earth; things made of "air" or "fire" tended to rise). These kinds of theories are unintuitive to us today, and easy to mock, but they are no more inherently unintuitive than "gravity is a force" or "gravity is what happens when mass warps spacetime."

Other phenomena we attribute to gravitation today includes the motion of the planets. This was understood both in terms of "natural" motion (per Aristotle) but also largely as a different phenomena than what you see from dropping things. There were separate explanations of how planets moved; they did not rely on attraction, but on crystalline spheres that the planets were locked inside of.

Newton's accomplishment was not "discovering gravity" but coming up with a very rigorous and quantitative framework that synthesized and combined a lot of research in mechanics, astronomy, and physics. He showed that all of the above phenomena were in fact manifestations of the same attractive force between masses. As for the nature of said force, Newton explicitly said he did not know — the math just works out if you imagine it is so.

The usefulness of this approach (by which comets, cannons, and the solar system can be understood in the same framework) was enough that people were generally won over by it and willing to overlook the mystery of the force. There were some who tried to come up with explanations of the force, such as Newton's protege Nicolas Fatio de Duillier, who imagined that all empty space exerted a "pushing" particle that forced things down ("push-gravity"), but none of these were extremely successful.

Einstein's General Theory of Relativity was the first really successful attempt to reframe gravity in non-Newtonian terms, though even it is considered to be incomplete in some important way (it does not reconcile with quantum mechanics correctly, so something is wrong there).

Anyway — the above is just a sketch but gives a sense of what Newton was really doing. "Discovering gravity" is probably the worst way to think about it, but it is a common way! "Unified mechanics and astronomy under the idea of universal gravitational force" is a better explanation.