They call them cowbirds because they were originally a plains bird that followed the buffalo (and later, herds of cattle) as they grazed. The cattle put up insects that the birds ate, and they'd be constantly on the move to keep up with the herds. This led to them becoming nest parasites--they lay their eggs in smaller birds' nests and let the smaller birds raise the cowbird young. Rather a nasty development but successful for the cowbirds. Eventually, with roads and farms and the clearing of forest areas, cowbirds spread into areas (like the forests around here) where they'd never been able to reach before and they're causing quite an impact on some of the small forest birds that haven't evolved to combat the cowbird's nesting strategy.
Since most baby birds are fed insects, almost any host will do--but the smaller (within reason) the host, the better, since (among other things) it allows the cowbird baby to out-compete the host's young for food when the adults come with supper....