Photons don’t have mass but they do have energy, and Einstein says that mass and energy are the same thing. That means they still have momentum and still impart force in a collision.
This effect isn’t just present on solar sails; if you stand in the sun (or in front of a light bulb, even) the light hitting you is imparting pressure on you, it’s just incredibly miniscule. Some cursory googling tells me the radiation pressure from the sun on Earth is about 10 micropascals, or about one ten-billionth the air pressure at sea level.
Even with such a tiny amount of force solar sails (theoretically) work because in space there’s virtually nothing to slow you down.
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