There are several species of Mulberry with edible fruit. The White mulberry is native to China, and its leaves are fed to feed silkworms. The Black Mulberry is native to Asia, and the Red Mulberry is native to North America.
The edible, juicy, blackberry like fruits are sweet but fairly bland and do not keep very well. They are not grown to any great extent commercially, due to the softness and perishable nature, but are available wild.
Mulberries are mostly eaten raw or used for jams and jellies. Black mulberries are the best tasting.