Essentially everything organic has phosphates in it. A few pool chemicals have phosphates, mostly some sequestrants. Plus in many areas tap water has phosphates in it.
Your phosphate level will tend to settle to a bit above your tap water phosphate level (due to continuing organics entering the pool balanced out by water replacement), unless you use a lot of sequestrant, or have a very high evaporation rate.
The chemical binds to the phosphates forming particles that cloud the water, and eventually get removed by the filter.
One thing they don't mention is that phosphate remover only removes some kinds of phosphate. There are other kinds, rarer, that can allow algae to grow regardless of phosphate remover. Having enough to these kinds of phosphate isn't all that common, but phosphate remover doesn't always work, even if you do spend the money. Plus if your tap water has a lot of phosphate, your chemical costs to keep phosphate down will be astronomical, not to mention lots of cloudy water.