what kind of tree?
It is a Persimmon. Yes, it is edible, but do not pick it until it is orange and soft. It is very bitter when green, but very sweet when soft and orange. They have 3-4 seeds per fruit and you will have to have a food mill to get the seeds out and to get the pulp to use for making cookies or bread. Raccoons and deer love them, so you have to beat them to the fruits. Persimmons are usually picked in Missouri in mid to late October.