To give a concise differential diagnosis for the whole of the Fungi is difficult. Definitions from D. L. Hawksworth, B. C. Sutton, and G. C. Ainsworth, Ainsworth and Bisby's Dictionary of the Fungi , Seventh Edition, 1983.
Fungi are hard to define.
Mostly, they are heterotrophic eukaryotes that feed by absorbing nutrients from their surroundings. Most are surrounded with a cell wall that contains chitin, and they have little ability to form tissues. Beyond that, they are a diverse kingdom of organisms, and are likely not derived from a single common ancestor. The Deuteromycetes are the asexual stages of Ascomycetes and Basidiomycetes. In many cases, we know how the fungus reproduces sexually, but since the asexual stage is more prominent, we commonly identify the fungus by its Deuteromycete name.