A tuxedo was a type of formal clothing worn mainly by Humans during the 20th century. A tuxedo usually consisted of matching coat and pants, typically black, a white shirt, and a bow-tie. They were considered very formal attire and normally only worn on exceptional occasions.
Odo assumed the appearance of wearing a tuxedo when he was in Vic Fontaine's lounge. He later morphed his clothing into a tuxedo shortly before rejoining the Great Link, as Kira Nerys thought he looked his best while wearing one. (DS9: "His Way", "The Sound of Her Voice", "Badda-Bing, Badda-Bang", "What You Leave Behind")
Nog wore a tuxedo while he was living in the holosuite and working in the lounge. Benjamin Sisko later wore one when he helped to rid the Bashir 62 holoprogram of Frank "Frankie Eyes" Chalmers. (DS9: "It's Only a Paper Moon", "Badda-Bing, Badda-Bang")