Most hydrozoans run a one-way life cycle: a settled polyp buds off a free-swimming medusa, the medusa reproduces sexually, and the medusa dies. Turritopsis dohrnii can run the last step backwards. A stressed, starved or damaged medusa contracts, settles onto a surface, and its cells transdifferentiate, converting from one specialised type to another, until the animal is a polyp again.
That polyp then buds medusae that are genetically identical to the original. In laboratory culture the reversal has been repeated across successive cycles, which is the basis for the word immortal. It is a real observation and it is unusual.
What the label overstates is the ecology. The animal has no defence against being eaten, infected, or simply failing to complete the reversal, and reversion is a stress response rather than a routine state. In the wild almost every individual dies as prey. The species is also small, a few millimetres, and drab, so its fame rests entirely on a cell-biological capability rather than anything visible in the water.