From ParagonWiki

A special event is a period of time during which the game is altered. There have been several primary kinds of events:

• Invasions, which usually entail a specific enemy group swarming Paragon City or the Rogue Isles (example: Rularuu Invasion Event 2004)
• Holidays, which usually include the implementation of special contacts, missions, badges, and activities that are only available for the duration of the event (example: Winter Event 2006)
• Anniversaries, which are held each year on the anniversary of the City of franchise (example: Second Anniversary Event)

Additionally, sometimes other events of community importance are referred to as special events, such as the Cuppathon.