Striker-fired pistols have a firing pin that is drawn into a retracted, set position as the slide travels from the rear position to the forward position. The striker is fully cocked by drawing the trigger to the rear and, at the end of the trigger stroke (break point) is released to fall on the bullet's primer. There is no hammer on a striker-fired pistol.
Pistols with a hammer have a free floating firing pin with a spring at the fore end to return it to the rearmost position after being fired. The firing pin is struck by the falling hammer that has been released by the pull of the trigger. The momentum of the striker ignites the bullet primer and the spring quickly returns it to the rear position.
I'll let someone else clarify if need be and elaborate on pro's and con's.