We can observe far away nebulae, outside our galaxy, using telescopes. We can also observe redshifts in light reaching us from them.
These redshifts are interpreted as being caused by the continuously increasing distance between those nebulae and earth.
Wherever we look in the sky, we find the distance between us and other faraway things is continuously increasing.
This is colloquially referred to as "things moving away from us" and "space is expanding", but the English language is not the appropriate medium to accurately describe such things and the meaning of words like "space" is not the same as we are used to in daily life.
So our primary observation is that distances seem to be expanding, which is then explained to laypersons by saying the universe is expanding, as well as more accurately among scientists by building conceptual and mathematical models to explain this observation.