The idea is that the Russian state taxes these landowners pay are based on the number of serfs (or "souls") on record. The problem is that many of these landowners must also pay for the serfs that have already died. It is these "dead souls" that Chichikov wants to buy from the landowners. He does not tell the owners why he wants the souls, but one can imagine that his plans are somewhat twisted. The novel is ultimately a social and political commentary...