It's constant because things like liquids and solids have a set type of structure (roughly, for liquids), and hence a set density. Water, the solvent, is a liquid. Adding another molecule of water is not going to change the concentration (much).
Another way to think of it is because we have heaps of water compared to any other species. In the reaction I'm consuming 1 molecule of water and 1 molecule of hydrochloric acid. Will we experience much change to the concentration of water? No, it'll still be high as, while the change in the hydrochloric acid concentration will be significant. It's sort of like taking 1 from 5, versus taking 1 from a 1 million.
On the other hand, aqueous substances and gases, have very variable concentrations.