Air ionization, positive ions
The plasmacluster supposedly works by ionizing water molecules in the air into $\ce{H+}$ and either $\ce{O^2-}$ or $\ce{HO-}$ ions. These ions then, supposedly, actively attach themselves to and break down pollutants, neutralizing their charges by pulling them apart. After they achieve this, the ions come back together to reform water.

At least, this is what their website says. They are correct that water can be split into positive and negative ions as well as the fact that these ions can come back together to reform water. I am unsure that the ions will stay separated from each other long enough to break up pollutants, and it is not very clear how positive and negative ions break up "pollutants." I find it unlikely that these ions will kill bacteria, which is one of the claimed benefits of this type of ionizer (I am not a biologist, so I could be wrong about this). Even if these ions are fatal for bacteria, odds are the plasmacluster cannot produce concentrations sufficient to do this. Also, if it could produce such concentrations, I might be somewhat concerned about what those concentrations of ions could do to humans.