Planck units are units derived from fundamental constants: gravtional (G), speed of light in a vaccum (c), Planck (h), and Boltzmann (kb) normalized to 1. They have the advatange of being 'natural' units rather than human defined. The kg was originally a defined standard, a human designated amount of material, if you use the Planck definition of mass mp=Sqrt( (h*c)/G)) everything is in terms of physical constants and thus less changeable/ subject to error.
The Planck mass works out to be relatively huge in terms of sub-atomic particles.
EDIT: Or rather, subatomic particles happen to REALLY small in terms of the 'natural' scale of mass.