lol! yes cocktail strainer. As in a Bond Martini "shaken not stirred"
you use it when you make a "shaken" drink; you shake the drink vigorously with ice, then rmove the shaker lid, cover the cup with the strainer, and pour the drink keeping the ice back. A properly shaken drink will immediately form a tiny little ice rust on top after being poured.
dang I guess you can tell I do drink lol!!