Parachutes work by increasing air resistance, which slows down the effects of gravity. Air is a gas, and though it is invisible, the molecules in the gas can still be used to help slow down a skydiver, much like water slows down a person who does a belly flop in water. Therefore, the air expands the parachute, providing resistance as the person falls.
When skydiving, people fall at about 125 miles per hour. The body's size already provides natural air resistance, which is why a person's speed does not keep increasing past this point. A parachute is a folded-up piece of lightweight fabric that is attached to the person by strings. When the person releases the parachute, it unfolds, creating a much larger area for air resistance than a person alone has.