DC provides a nice steady flow of power and is reasonablly easy to design motors for but it is a PITA to voltage convert and the motors have to contain either a brush assembly that wears down with age or complex electronics.
Single phase AC is easy to voltage convert but delivers power in a varying pattern (which causes vibration in motors and generators) and is tricky to design efficiant motors and generators for.
Three phase AC to a large extent brings us the best of both worlds. By having three lines all varying in the same way but out of phase with each other we can keep the power flow constant and we can also create a rotating magnetic field directly from the supply which makes it much much easier to design efficant motors for.