Smart host is a term describing a mail server that is used as an email relay by another server.
MTA implementation using smarthost is significantly simpler (both in implementation and configuration) than a full MTA with delivery according to MX-records in DNS , therefore such MTAs are used on non-mail servers in organizations that have a dedicated mail server ( or such is provided by the Internet / hosting provider ), in small organizations (relying entirely on the provider's servers).
The server used by the mail client ( MUA ) for sending SMTP emails can be considered a smart host for MUA, although, in this case, this term is not used.