People were well aware of what we now call gravity. Perhaps the most well-known and most influential explanation for the phenomenon was the Aristotelian physics. In this system, all bodies strive towards their natural place in the universe. In other words: everything in the universe has its place, and everything actively moves towards that place.

Now, for Aristotle there are four elements: fire, air, water and earth. Of these, earth is heaviest because its natural place is in the center of the universe. Water is a bit lighter than earth, because its natural place is above the earth. Air strives to be above the water, and fire strives to be above the air. In this way, everything has its place.

Of course, real objects are composed of multiple elements, and our world is too chaotic for such a neat distinction. The world is a complex mess, but everything in it still strives for its natural place.

Furthermore, do not confuse the mathematical laws, with the explanation of the phenomenon. We have always had explanations of why things fell down. That is not something Newton discovered. Rather, Newton provided a mathematical description of gravity. His theory, however, does not give any explanation at all. Famously, Newton refused to speculate on what causes gravity.

If you want to learn more about medieval physics, I highly recommend Edward Grant's The Foundations of Modern Science in the Middle Ages, Cambridge University Press, 1997. Specifically, he explains the Aristotelian theory of gravity on pages 59-61.