A Hosted wallet is an online service where a user’s bitcoins are stored, and they can send and receive bitcoins from this service. Coinbase, Bitflyer, and Mt Gox are examples of hosted wallets.
In their Interpretive Letter #1172, the Office of the Comptroller of the Currency (OCC) defines a hosted wallet as “an account-based software program for storing cryptographic keys controlled by an identifiable third party. These parties receive, store, and transmit cryptocurrencyA cryptocurrency (or crypto currency) is a digital asset des... More transactions on behalf of their accountholders; the accountholder generally does not have access to the cryptographic keys themselves.”