The marine animal group with cube-shaped medusae that includes box jellyfish is Cubozoa.
The name comes from the box-like bell of its medusa, or free-swimming adult form. Unlike many drifting jellyfish, cubozoans are active swimmers and can hunt small fish and crustaceans. Their bell's inward-folded rim helps produce a powerful jet of water.
Cubozoans are cnidarians, related to true jellyfish, sea anemones and corals. They are not simply another order within Scyphozoa: taxonomists recognized Cubozoa as its own class in 1973 because of distinctive morphology and life-cycle features.
A common mix-up is treating “box jellyfish” as one species. It is a broad common name for many species, including the dangerous Chironex fleckeri and the much smaller Irukandji jellyfish. Box jellyfish also have unusually complex visual systems: each of four sensory structures can carry six eyes, for 24 eyes in total.