Liquid Neutronium is, as the name implies, a liquid form of neutronium.
Neutronium itself is degenerate matter where quadrillions of atomic nuclei are fused together into one gigantic super-nucleus, mostly consisting of neutrons, with a few protons unwillingly bound in by the incredibly powerful strong-force field, all suffused with a sort of electron soup flowing in and among the nucleons instead of orbiting them in distant clouds like in individual atoms. It is incredibly dense, weighing in at approximately one mountain per barely-visible-speck. It can only exist inside powerful gravitational and magnetic fields that help the strong atomic force hold it together against the incredible repulsive force of even the handful of surviving protons.
How does this in turn become liquid? Screwing with the laws of physics on that scale pretty much requires magick. Why would one do such an insanely dangerous thing as create a vial of liquid neutronium, let alone a few thousand gallons of the stuff?
Because it's incredible density lets you use it as the basis for all sorts of reality-warping, gravity-warping devices. The Jump Accelerator Rings used in the experimental drive systems on board the INS Alistar Dimiye are filled with liquid neutronium, for example. It's also part of the internal plumbing of a Gravitic Ram, and probably involved in the makings of a Gravity Drive in general, including in Jumpgates and Hyper Generators.
Behind the ScenesEdit
Believe it or not, the stuff inside neutron stars, or "neutron degenerate matter" as scientists refer to it to avoid confusion with a few other things that have been called "neutronium" over the years, is actually a fluid, although closer to a plasma than a true liquid. Either way, it's not something you can handle in pipes without it explosively decomposing into individual neutrons the picosecond it's no longer under neturon-star-interior-level pressures. Handling it is probably beyond any realistic level of technology in the TI universe, but Martin likes to use it in his technobabble rather than simply outright waving his hands and saying "magick".