Incredibly dense matter of the kind found in neutron stars, virtually impervious to weapons, which forms the hull of the planet killer in The Doomsday Machine.
Neutronium is matter compressed to enormous density, as in the core of a collapsed star. In Star Trek it is used by only the most advanced builders, and almost nothing can cut or blast through it.
It is introduced in the Original Series episode The Doomsday Machine, where the planet killer's hull is solid neutronium and shrugs off phaser fire, so that the machine can be destroyed only from within.
Later examples include the Dyson sphere found by the Enterprise-D in The Next Generation episode Relics, whose shell is made of carbon-neutronium, and the reinforced doors guarding the Iconian gateway in the Deep Space Nine episode To the Death. Neutronium alloys and armour are also mentioned in Voyager.