Parachute pants refers to two distinct styles of pants that were popular between the 1970s and 1980s.
In the 1970s and early 1980s parachute pants was the term used to describe a pair of pants constructed out of a heavy nylon. These pants were first made popular by brake dancers who needed durable pants that could handle the abuse of breakdancing while at the same time be slick enough to reduce friction with the ground while performing certain dance moves. Typically these pants were fairly formfitting though not excessively tight.
From the mid-1980s to the very early 1990s parachute pants transitioned into a new style entirely. The construction material switched from being solely out of nylon to a more diverse palette of typically synthetic fibers, and were made in much brighter neon colors. Additionally the fit of the pants changed dramatically. Whereas parachute pants were once formfitting they became quite voluminous around both the upper and lower leg; with the apex of the puff typically around the knee. The volume effect of these pants was further emphasized by an elastic band or drawstring that was used to keep the pants snug around the ankles. This incarnation of parachute pants was worn for fashion rather than functional purposes.
Today parachute pants are almost never seen as they vary rapidly went out of fashion in the early 1990s - and unless you are dressing for an 80s theme party will not make a good addition to your wardrobe.