A barbecue is a style of food preparation on Earth, which typically consists of cooking a large slab of meat over an open fire pit. Those from Texas, in the United States of America, are well-known for putting on lavish Texas barbecues.
Tucker complained that he caught the three Takret that were aboard Enterprise "throwing a barbecue next to a plasma manifold." He stated that he understood that the crew were explorers and that they were "supposed to keep an open mind about different cultures," but that the three Takret they had aboard with them were driving him crazy. (ENT: "The Catwalk"}
The mother of formerly assimilated Starfleet officer Riley Frazier was known for her famous Texas barbecue. After Frazier was freed from the Borg Collective she had recurring dreams of her mother's barbecue. Prior to Chakotay's departure from the planet where she lived, he offered to replicate her some Texas barbecue, but noted that it probably wouldn't compare to her mother's. (VOY: "Unity")