As NASA and Tom Speer (a Boeing aerodynamicist who also designs the wings for the winning US America's Cup team) says, there are basically a bunch of different ways to explain the way sails and wings work. Each of these ways is as correct as the other, essentially. There's also some wrong ways, like the "equal time" concept.
See
www.grc.nasa.gov/www/k-12/airplane/right2.html The "Newtonian lift"/lift from flow turning" theory works best for me. The sail redirects the wind and shoves it out the back. As Isaac Newton said, a force creates an equal and opposite reaction, therefore shoving air out the back shoves the rig forward.
Sure, there is laminar flow, attached flow, boundary layer effects and all that - but they are really about ensuring that the flow moves across the sail efficiently, rather than breaking down into turbulent flow which moves more slowly and less uniformly and therefore you shove less air out the back, and at a lower speed.
Look up Tom's posts on Boat Design Forum. Also look out for Mark Drela, a professor of aerodynamics at MIT and designer of America's Cup wings and world-record human powered aircraft and boats. Those guys really, really know their stuff - and unlike a lot of the stuff around, the theories they speak of also work in real life.