And it transfers that momentum to the sail, right?
If photons had mass, then as they passed through our cells, they would be like radiation, damaging them. If it had mass, windows probably would not let as much light through and would be very reflective.
To understand the trapping of light in a black hole, imagine the idea that gravity is like a dip in spacetime. The photon hit's the dip and cannot get out, like a coin in one of those wishing well thingies that sends it spinning around the rim of the hole, until it vanishes and cannot escape.