The basic difference is that a pentaprism is a solid block of glass. This means it's fairly heavy. It has mirroring material on all but two sides, so the light enters one side, gets reflected around inside, and then comes out the one other un-mirrored side. This means there are only 2 air/glass interfaces involved: one where light enters the prism, and one where it leaves the prism. This keeps light loss to a minimum.
A pentamirror does pretty much the same thing, but it's composed of a number of separate mirrors, so there's air in the middle instead of a block of solid glass. This makes it considerably lighter and less expensive. It also means there's an air/glass interface for each individual mirror, so there's quite a bit more light loss.
As a result, a pentamirror is used almost exclusively in relatively low-end cameras where reduced expense and weight matter more than a relatively dim view through the viewfinder.