The captain's yacht was a large auxiliary craft docked in the underside of the saucer of some Starfleet ships, intended for diplomatic errands and seen in use on the Enterprise-E.
A captain's yacht is a vessel bigger than a shuttle that fits flush into the bottom of a starship's primary hull. The Galaxy class was designed with one, visible as an oval shape beneath the saucer of the Enterprise-D, though it was never launched in The Next Generation. Behind the scenes it was given the name Calypso.
The only yacht used on screen is the Cousteau of the Enterprise-E in Star Trek: Insurrection. Picard, Data, Worf, Crusher and Troi take it down to the Ba'ku planet with weapons and supplies when they decide to defend the villagers against removal.
Both names honour the oceanographer Jacques Cousteau and his research ship. Voyager's aeroshuttle, also never seen in flight, was planned as a similar craft.