Fungi are a kingdom of organisms which share the following characteristics:
Their main body is in the form of thin (one cell thick!) strands called mycelium (bottom left in the picture).
They cannot manufacture their own food through photosynthesis; rather, the mycelium secretes enzymes which digest part of their surroundings (a log, for example) and this is then absorbed by the mycelium.
Their cell walls are made mostly of chitin and similar compounds, not cellulose.