The basic difference is that a pentaprism is a solid block of glass. This means it's fairly heavy. Light enters one side, gets reflected around inside, and then comes out one other 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.