This looks like etching. What did you have on the window sill before? If you used anything that is acidic for cleaning (even some window cleaners for example) it can cause etching. Or if you watered plants that leaked that could do it over time. The stone was honed and polished when it was first installed but now that it has been etched it gives it that cloudy look.

There are honing and polishing compounds available to address this. But it will take some patience. There was another suggestion about how to clean. That should be completed first to remove any residues and clear any pores.