Box jellyfish belong to the class Cubozoa, and are not a true jellyfish (Scyphozoa), although they show many similar characteristics.
The bell or cube shaped jellyfish has four distinct sides, hence the box in the name.
When people talk about the extremely dangerous Australian box jellyfish they refer to the species Chironex fleckeri. This is the largest box jellyfish species.
The other species that is known to have caused deaths is Carukia barnesi, commonly called Irukandji. This one is a tiny jellyfish, only about thumbnail size. I talk about Irukandji here.
There are other species and not all are poisonous. (From here on, if I say box jellyfish, I am referring to Chironex fleckeri.)
A fully grown box jellyfish has a respectable size: it measures up to 20cm along each box side (or 30 cm in diameter), and the tentacles can grow up to 3 metres in length. Its weight can reach 2 kg.
There are about 15 tentacles on each corner, and each tentacle has many thousand stinging cells (nematocysts). The stinging cells are activated by contact with certain chemicals on the surface of fish, shellfish or humans.
Box jellyfish are transparent and pale blue in colour, which makes them pretty much invisible in the water. So much so that for years nobody knew what was causing swimmers such excruciating pain, and sometimes killed them.
The box jellyfish propels itself forward in a jet like motion and can reach three to four knots, that's 1.5 to 2 metres per second. (True jellyfish in contrast rather drift.)
Box jellyfish can see. They have clusters of eyes on each side of the box. Some of those eyes are surprisingly sophisticated, with a lens and cornea, an iris that can contract in bright light, and a retina.
Their speed and vision leads some researchers to believe that box jellyfish actively hunt their prey, others insist they are passive opportunists, meaning they just hang around and wait for prey to bump into their tentacles. They certainly are very good at avoiding even tiny objects and probably at least try to avoid humans, too.
Box jellyfish venom is very different from the venom of the true jellyfish. More on the venom and its effects below.
Chironex fleckeri have caused at least 63 deaths in Australia since 1884. (Irukandji caused two that we know of.)