What happens
With a selective membrane between two solutions, water responds to the difference in chemical potential on each side. In a simple dilute case, the net movement is toward the more concentrated solution.
Where do we see it?
Water molecules still cross in both directions. Osmosis describes the net balance, not a one-way gate. A pressure difference can eventually balance the tendency to move.
Cells constantly deal with osmotic effects. Reverse osmosis applies pressure to push water through a selective membrane, for example in desalination.
A little further
Osmosis is therefore not a simple mechanical filter. The membrane, the dissolved species, concentration and pressure all matter.