Fungi are neither plant nor animal, but a separate category of creature, closer in some ways to animals than to plants.
At school most of us were taught that there are two kingdoms within nature; plant and animal, and that fungi (mushrooms, toadstools etc), being creatures that are stuck in one place, definitely belong to the plant kingdom. However, fungi are strange plants; they have no roots and do not contain any chlorophyll. This initial belief originated with the Greek thinker, Aristotle, and it was then carried-on through the Middle Ages and adopted by the great botanist, Linnaeus. But it is wrong. There are several kingdoms (taxonomists argue about precisely how many). To the previously mentioned kingdoms, we can add fungi, seaweeds and several other microscopic based categories. Perhaps it is a matter of language; the technical name is fungus (plural fungi). The words mushroom and toadstool are popular names, mushroom denoting a fungus that you can eat, toadstool denoting one that you cannot.
Unlike plants, fungi are air breathers, and farmed mushrooms deprived of an air flow become small, brown and inedible. Whilst plants have roots, fungi have hyphae, a large network of threads that absorb nourishment from the soil. A vital difference is that while the plant that you see above the ground is the main part of the creature, the fungus that you see is merely the fruit. The bulk of the fungus lies below ground in a huge network called the mycelium. The visible fungus that you see is to the mycelium what the apple is to the tree.
Many fungi work symbiotically with plants. These are known as mycorrhizal fungi. They weave themselves into the root environment and vastly widen its surface area. This means that they can draw minerals from the soil, some of which are passed onto the plant. In return plant sugars, made by photosynthesis, are sent down to the fungi. As fungi cannot make sugars themselves, or they make them with great difficulty, this is an important contribution. It is the fact that fungi are not plants that enables them to work symbiotically with plants. Their differences make them complementary, in many cases, though there are some parasitic fungi that damage plants, such as honey fungus which damages trees.