From YPPedia

A party is an event where a notice can be displayed for a fee of 250 PoE. The notice is placed on the island's notice board together with a link that can whisk players to a specified location.

The event is created by clicking on the "Throw Party" button in the "Shoppe" or "House" tab by the owner, manager or roommate. The player can specify a message and it will be displayed on the notice board of the current island for one hour.

A close, but entirely different event is a parrrty, which is a real life event hosted by Three Rings.