In home improvement, a project that adds minimal value to the home (and may actually decrease home value) and is undertaken on the whims of the homeowner. Usually done by someone with too much money on their hands. A DIY project, no matter how odd, typically doesn't qualify as a vanity project if they actually work on it themselves.
My rich uncle's latest vanity project was getting the solar panels ripped off his roof and replaced with a replica of Kennedy Space Center for his model rockets.
My trustifarian friend had a brand new kitchen demoed in the home she just bought because she thought it was too suburban looking. The granite countertops are just sitting outside if anyone wants them.