Metallic hydrogen (aka conductive hydrogen) is a state of hydrogen that is theorized to occur at very high pressures (millions of atm). It is termed metallic in the ordinary non-astrophysical sense of a material that easily conducts electricity. It is presumed to be solid at lower temperatures and liquid at higher temperatures. There are attempts to produce it in the lab but the required pressure is difficult to produce and there has been no unequivocal success. The equation of state (EoS) of metallic hydrogen is currently theory, thus of research interest.
Jupiter and Saturn are made of substantial hydrogen, much of it under enough pressure to be metallic. It is assumed that these two reservoirs constitute the majority of the matter in the solar system if the Sun is excluded. It is believed that heavier elements and compounds can be dissolved in metallic hydrogen, and it is possible Jupiter's center consists of such a solution rather than a solid core.
I believe the hydrogen of stars is not considered metallic, but I'm not sure why and speculate it might be a question of semantics. As more about metallic hydrogen's EoS is determined, use of the terms might change.