A mascot was a person or object intended to represent or bring luck to a certain establishment.
Quark considered Morn to be his bar's mascot, going as far as to replace him with a hologram at one point, because, according to Quark, "Everyone who comes in here expects to see him, and if they don't, it doesn't feel like home to them."
After Morn faked his death in 2374, Odo remarked that without Morn as a mascot, business would suffer. (DS9: "Who Mourns for Morn?")