Algae removes nutrients out of the water column as it grows, just like a plant. So nitrates, phosphates, ammonia, etc. It's pretty much as simple as that.
I don't have personal experience with freshwater scrubbers, but I know several who run them. The algae grows thinner/finer than in saltwater, where you typically see them used. Depending on your system, they can reduce nitrates quite well, but if your tap water is a high source of nitrates then you're just keeping on top of the battle.
There are plenty of things you can do to "improve" your scrubber, building it right in the first place is the best though