Even when you get a parasite that can develop in a large number of different hosts, the parasite usually develops best in one or two host species and less readily in the rest. However, the vast majority of parasites are restricted to one or a few closely related host species, and this is what is meant by host specificity.
Host specificity can of course be different at different stages of the life cycle.
The digeneans, for example, are highly specific for their molluscan host, but much less so for their vertebrate host. Host specificity can be supra-specific , where natural groups of parasites are associated with natural groups of hosts. For example, Gyrodactylid monogeneans are always found on Cypridont fish. Host specificity can also be infra-specific , where a single species of parasite is associated with single species of host. However, the greatest diversity of monogeneans is found on teleosts, and whilst many species are found on elasmobranchs, only a few occur on amphibians and reptiles.