Both polyps and medusae have a body plan with a basic radial symmetry. Thus unlike a bilateral organism like a fish or person, similar repeated components of the body are arranged around the central body axis. All cnidarians are endowed with nematocysts , microscopic stinging and sticky structures used primarily for prey capture. This characteristic is a uniquely defining trait of the phylum. Cnidarians are at the tissue level of organization - they lack any structures that can truly be called organs, like a heart or brain.
True jellies are only part of the gelatinous zooplankton menagerie, however.
All make ends meet without the benefits of a hard skeleton or tough tissue. Lacking dense bodies and hard body parts does have its advantages. Some gelatinous animals, like the sea nettle, Chrysaora fuscescens and the purple-striped jelly, Pelagia colorata , make conspicuous sojourns into nearshore waters on a sporadic basis. Most types lead far less splashy lifestyles, however, and are overlooked by most people. Don't count on seeing any of these delicate creatures on your next ocean excursion however.