What is a gyre? Where would you find one?
A gyre is a vortex of gas or liquid.
In terms of oceanography (since that is where this question has been asked) it refers to any large system of rotating ocean currents.
A typical example would be the North Atlantic Gyre which flows North along the coast of North America, then East, South down the Coast of Europe, and then back West along the edge of the tropics.