Neutrino-ion generators are power sources used by the Asgard primarily to power their starships. While there is no information whatsoever regarding how these devices work, one can assume, by its name, that it works in a manner similar to the naquadah generators of the Tau'ri, but instead of naquadah it uses an unknown material which was later changed to use the more unstable naquadria. (SG1: "Nemesis")
Behind the scenes
While many fans assume that the neutrino-ion generators use either neutrinos or neutronium, Stargate SG-1: The DVD Collection 22 states that the O'Neill-class ship uses naquadria—though misspelled naquadriah in the magazine—in its generators, which is an upgrade from a material which, at that time, was not named in any source. According to Stargate Atlantis: Nightfall, however, the generators use neutrinos from a protostar. As the ship in this novel had been cut off from the Asgard for thousands of years, we can assume that this is the previous material.
The picture shows the command bridge of the Biliskner, not the Neutrino-Ion-Generator. The Generators are only visible on the outside of the ship below the main hull. The long blue glowing line below the hull is separated by 4 clearly visible generator-like structures.