When you jump out of an airplane, you experience two forces: gravity and air resistance. Gravity pulls you down towards the ground, while air resistance pushes against your body as you fall.
A parachute increases your air resistance as you fall, slowing you down and allowing you to arrive to the ground without splatting into a pancake. When you pull the cord that opens the parachute, the expanded parachute's area catches air, slowing you down.
A simpler way to put it is that an object with a bigger area will move slower, while an object with a smaller area will move faster.
When a skydiver jumps out of a plane, his velocity increases, when he stretches out his arms it slightly decreases, and when he activates his parachute, he reaches terminal velocity, which is a constant until reaching the ground.
Area = Area of the part of the object facing down.