Like plants, they have a cell wall, which is a durable framework that supports the cell, which animal cells do not have. Unlike plants, this cell wall is made of chitin rather than cellulose. Animals though use chitin to make hard shells, which is what insect exoskeletons are made of.
Fungi reproduce similar to how simple plants do, by spores. Yet they cannot synthesize their own food like plants can. Like animals, they have to take in food. However, they are also immobile for the most part, like plants. They rely on the environment to move around, where as even simple animal cells can move on their own power.
So they have attributes of both, but are not quite one or the other.