The Baraka was a replica of a Bajoran Shabren-class lightship constructed by Benjamin Sisko in 2371. Its name comes from the Swahili word for "good fortune". (CCG reference: Tenth Anniversary Collection)
Sisko began construction of the ship on Deep Space 9 after returning from Bajor with schematics of the original lightships. He only used tools and materials the Bajoran shipbuilders would have possessed, although he did add artificial gravity plating so it would be easier for him to pilot the ship.
The Baraka was later launched from the space station and set course for the Denorios Belt. During the journey there, one of the solar sails was damaged, but Benjamin and his son Jake were determined to press on. The ship was continuing on its course when it hit a tachyon eddy. The phenomenon accelerated the Baraka to warp speeds, reaching the Cardassian system in a matter of minutes. Having proved the ancient Bajorans could travel to Cardassia using the same method, the Cardassians (in the from of Gul Dukat) were forced to admit they had discovered several lightships on the surface of Cardassia. (DS9 episode: "Explorers")
Sisko kept the Baraka at Deep Space 9 for at least a year. In 2372, he planned to take a trip in it with Kasidy Yates. However, their trip was called off when a plasma storm hit the Bajoran system. (DS9 novel: The Tempest)
Sisko recalled the voyage of the Baraka later that year. Jake would also recalled the journey, in late 2375 after his father had fought Dukat in the Fire Caves and joined the Prophets. (DS9 novel: Trial by Error, DS9 episode: "What You Leave Behind")
Thirishar ch'Thane had read about the Baraka prior to the Gateways Crisis in 2376. Nog had recalled the Baraka's encounter with the tachyon eddy when they were investigating why there were no Iconian Gateways in the Bajoran system. (DS9 novel: Demons of Air and Darkness)