How does the universe expand?

I think you are asking how the universe expands, as in, if the universe is everything, then what is it expanding into? The best way to answer this is to picture a two-dimensional universe, whose surface might resemble a sphere if it were wrapped around itself and joined. If you then inflate that sphere like a balloon, it expands. Any two-dimensional being that lives on that surface would not be able to see the expansion of the sphere, only that it is expanding. This is because the sphere is expanding into the third dimension.

All you need to do now is add a dimension, and the fourth dimension will explain how a three-dimensional universe is expanding.

In our universe, we see that gravity is able to bend space; when light travels near a very large body (like the sun), we see that the sun's gravity can actually bend the light. Additionally, the way black holes behave—gravity so strong that light cannot escape—further demonstrates this model. If you press your finger into the surface of the sphere, you create the equivalent of gravity. In that case, gravity is actually bending the space.

The universe expands due to the phenomenon known as cosmic expansion. This expansion is driven by the increase in the scale of space itself. It is described by the theory of general relativity, which predicts that the distances between galaxies increase over time. This expansion is not limited to the galaxies themselves but affects all of space, including the empty regions between galaxies. The expansion of the universe is currently accelerating, attributed to dark energy, a mysterious form of energy that permeates space and exerts a repulsive force on cosmic scales.