The naming of organisms is an important part of how we communicate. When a fungus is found, be it a mycelium from a rotting fruit, a mushroom from the forest, or something growing on a petri dish, we have used morphological and other phenotypic characteristics to group them together and identify if it is an already known species or a new one. However, some fungi have very different shapes and forms that occur during asexual and sexual (after mating with a partner) stages, some incredible elaborate and even (to some people) beautiful. Because these stages mean that fungi can look very different, and often these fungi are not amenable to life in the laboratory (e.g. we can’t get it to complete the lifecycle in an petri dish in the lab), it was the case that observed asexual (or anamorphic) and sexual (teleomorphic) forms of a species get different names. For some species, connecting the two forms has eluded mycologists, and those which had a lack of a sexual stage were called Fungi Imperfecti. Some fungi are only thought to have an asexual stage, though that may change as more molecular and other data is developed.
http://fungalgenomes.org/blog/2011/08/one-fungus-one-name/