A "parachute" is the generic name for a style of dry fly. Rather than having hackle wound around the hook shank, perpendicular to the shank, the hackle is tied above and parallel to the shank around a post made of hair or foam or other materials.
Two things seem to be accomplished by this style of dry fly:
1. The fly's body sits in the surface film, rather than hovering above the surface; and
2. The hackle tips leave a more realistic impression on the surface as viewed by the trout below.
Some people prefer parachutes anytime trout are surface feeding. Others feel they are most effective when trout are grabbing the emerging or "stillborn" duns. I have found them to be effective also during spinner falls. I usually carry typical "catskill" duns and parachutes and if one isn't working, I'll try the other.
Trout are stupid and they do stupid things for stupid reasons, so you have to be versatile.