Well honestly due to the fact this is the first piece of gear to refer to it as "Quick Magic" rather than "Occ. quickens spellcasting" I understand the confusion.
Quick magic is when you instantly cast a spell. A spell cast with this ability proc has a recast time of 0.
It was introduced back in Abyssea.... And has been around for a long while now... Ogapeppo Cape, Impatiens, even Moonshade Earring all carry this augment.
EDIT: While this was the first piece of gear, the help text was first used on the Atma of the Apocalypse.