From TARDIS Index File, the free Doctor Who reference.

The Mary Celeste (sometimes incorrectly spelled Marie Celeste) was a cargo ship captained by Benjamin Briggs. In 1872, a month after it left port in New York City, it was discovered in the Atlantic Ocean, completely abandoned. The fate of the crew and passengers was never discovered.

The nameplate of the abandoned ship, identifiying it as the Mary Celeste

The Doctor, Ian Chesterton, Barbara Wright and Vicki arrived in the Doctor's TARDIS on board the ship while being pursued by the Daleks in their DARDIS. When the Daleks arrived on board, the crew were so frightened of the Daleks, who they mistook for "the Barbary Terror" that they jumped overboard rather than face them. The Doctor was unaware of the name of the ship he had landed on. (DW: The Chase)

Other contradictory accounts

• The Doctor, Jamie McCrimmon and Zoe Heriot found that the crew of the Marie Celeste had been abducted by Arcturans. The Doctor freed the crew, but they were then all killed by a sea serpent. (DWA: The Mystery of the Marie Celeste)

• When the Doctor landed the TARDIS on the New York docks, the crew mistook it for cargo and had it loaded on board. To regain access to his ship, the Doctor paid for passage on the Marie Celeste. When he showed Professor Theodore Cassells the TARDIS interior, he fled from the hold to the deck. When he tried to tell the captain what he saw, the captain misunderstood and thought the TARDIS was a time bomb. He, Cassells and the crew left the Marie Celeste in a lifeboat, which was swamped by a large wave that drowned everyone on it. The Doctor left, unaware of the name of the ship he was on. (However as this ship used the spelling Marie Celeste on its nameplate, it may have been a different vessel.) (TVA: A Stitch in Time)

Behind the Scenes

The true reason for the desertion remains unknown.

Wikipedia has a more detailed and comprehensive article on

Mary Celeste

Memory Beta, the wiki for licensed Star Trek content.

The Mary Celeste was an old Earth "ghost ship" legend. She was a brigantine found in the Atlantic Ocean unmanned and under full sail heading towards the Strait of Gibraltar in 1872. The fate of the crew is the subject of much speculation: theories range from alcoholic fumes to underwater earthquakes, and there is a large number of fictional accounts.