In brief, Warm Dark Matter (WDM) is one of the solutions to the problem of the missing mass in the Universe.
When observing large scale structures in the Universe it is apparent there there is not enough visible mass to explain the rotation and binding forces that seem to hold everything together.
This problem has one of two solutions: either our theories of how matter interacts is flawed (possible, but not widely accepted) or there is a significant amount of mass present in these structures that is invisible - i.e. does not interact with other matter via the electromagnetic force.
What is Warm Dark Matter (WDM) and Neutrinos
Assuming that there is a significant amount of mass that we can not see, researchers have arrived at three explanations of what this missing mass may be.
One solution is Warm Dark Matter (WDM). One type of proposed WDM is the sterile neutrino. Such a particle would be similar to other neutrinos in that they don't interact with other matter via strong or electromagnetic forces, but do via the gravitational force.
The difference is that while normal neutrinos also interact via the weak force - the cause for decay of neutrons into protons - the sterile neutrino would not.
This would allow the sterile neutrino to take on a much larger mass than normal neutrinos; important when discussing the amount of neutrinos that would be needed to explain the mass deficit.
Similar neutrinos are also popular among theories of Hot Dark Matter (HDM), but those neutrinos by necessity of their creation travel at near light speed. Sterile neutrinos on the other hand would not be constrained in such a way.
Gravitinos
Another possible candidate for Warm Dark Matter is the gravitino.
While the photon is the force carrier for the electromagnetic force and the graviton (still un-observed) is the force carrier for gravity, the gravitino is the force carrier for supergravity interactions. (Supergravity is a theory designed to combine general relativity with the principles of supersymmetry.)
Supergravity interactions are still unproven. But should this change than their force carrier would be an excellent candidate to explain some of the missing mass in the Universe.
Weakly Interacting Massive Particles (WIMPs)
Weakly Interacting Massive Particles (WIMPs) share much in common with neutrinos, except that they are much more massive and, therefore, move more slowly.
They are a favorite solution to the dark matter problem because they have everything you could want - massive, slow moving and weakly interacting so they can't be "seen". The only problem is that such particles have never been observed.
Perhaps more troubling no one is quite sure what a WIMP actually is. In order to find out, several experiments have been devised to try and direct WIMPs, both directly and indirectly.
WIMPs, however, are thought to likely arise out of thermal reactions (i.e. during processes with high temperatures). Such mechanisms would place WIMPs in the category of Cold Dark Matter (CDM). So in order to be considered WDM, the WIMPs would have to be created though non-thermal means.
It is not entirely clear if this is possible, since the exact nature of WIMPs is unknown.
