A minesweeper is a small naval warship

Warship

A warship is a ship that is built and primarily intended for combat. Warships are usually built in a completely different way from merchant ships. As well as being armed, warships are designed to withstand damage and are usually faster and more maneuvrable than merchant ships...

 designed to counter the threat posed by naval mine

Naval mine

A naval mine is a self-contained explosive device placed in water to destroy surface ships or submarines. Unlike depth charges, mines are deposited and left to wait until they are triggered by the approach of, or contact with, an enemy vessel...

s. Minesweepers generally detect then neutralize mines in advance of other naval operations.
In Britain naval leaders recognized before the outbreak of World War I that the development of sea mines was a threat to the nation's supply and began efforts to counter the threat. Sir Arthur Wilson noted the real threat of the time was blockade aided by mines and not invasion.