Filtration removes solids from a liquid or gas in which they are dispersed. Solutions have substances dissolved in them, but not dispersed.
Filtration allows a solid product to be removed from a liquid or gas in which it has been dispersed. "Dispersed" means that it may have been broken down into small fragments or particles, but still remains as a distinct second phase within the liquid or gas. This is quite distinct from "dissolved" which denotes that a substance has formed bonds with the liquid or gas so as to form a single-phase.
A dispersion of solid in liquid such as clay in water can be filtered to remove the clay provided the mean size of the majority of the particles of clay is larger than the pore size of the filter medium. The water passes through, and a certain % of the clay will remain on the filter.
But attempting to filter a solution, such as salt water, doesn't result in any separation of the salt. That's because salt in aqueous solution does not have any solid structure and exists only as solvated ions. Everything in the solution has dimensions on the ionic or atomic scale, so irrespective of how fine your filter medium is, the whole solution passes through.
There are exceptions...a saturated solution that may have (some) undissolved solid salt in it - the undissolved salt can be filtered out. Also, polymer solutions are a different case, as the large molecular size can make a difference in some cases.