Effect Item is a common name for "items" that aren't actually items.
In general, Effect Items do not appear in inventory. Instead they are represented by an icon at the top of the screen. They are always active, no equipping takes place. They cannot be dropped or destroyed, but some are lost after entering a battle or a few, or after losing one.
A maximum of 5 status effects can be shown at once; in the above example, there is visible The Sarapox, Mister Penguin, Al Howin Gobball Transformation, The Lurgi, and Tingo, while Tingo obscures Zombie using the same image.