The expansion of the universe is often described as the stretching of the fabric of spacetime. While this depiction is accurate in certain respects, it obscures the simplicity of the concept and makes it sound more mysterious than it is.
The expansion is nothing other than objects thrown away from each other in otherwise empty space.
To understand this, it is useful to think about the composition of the universe.
On large scales, the universe consists of ordinary matter and radiation, dark matter, and dark energy. For the purpose of this discussion, we will set aside dark matter and dark energy and focus on the visible content.
At present, this visible content is primarily organized into galaxies and intergalactic gas. For simplicity, we can think of the universe as a collection of galaxies distributed throughout space.
On large scales, the universe is homogeneous and isotropic to a good approximation. This means that an observer in any galaxy would perceive the expansion in essentially the same way.
In such a setting, there is a unique large-scale pattern of motion: every pair of galaxies moves away from each other, with a relative velocity proportional to their separation.
This is the Hubble law.
There are two equivalent ways to describe this situation.
One can think of galaxies as moving through space, gradually increasing their separations.
Alternatively, one can describe them as fixed in place while spacetime itself evolves in such a way that distances between them increase. This is often visualized by imagining galaxies as points on the surface of an inflating balloon.
These are not different physical processes. They are two ways of describing the same underlying behavior.
The expansion of the universe does not require anything exotic.
It is a large-scale pattern of motion in which distances between galaxies grow over time. In this sense, forming an expanding universe amounts to placing objects in motion so that they move away from each other.
On smaller scales, this behavior is not observed.
Galaxies participate in the expansion as a whole, while their internal dynamics remain largely unaffected. Stars orbit within galaxies, and planetary systems and atoms remain bound, with little regard for the large-scale motion.
A useful analogy is that of a train: the train may be moving in one direction, but people inside are free to move independently, largely unaffected by the motion of the train itself.