A tea cozy is a padded mitten for your tea pot to keep it warm. Tea cozys range from the practical (a drab and austere, rectangular piece of cloth) to the whimsical (usually a garish and elaborately stitched chicken or some other farm animal.)
Being asian, I never really saw the need for tea cozys; most asians I know get a pot of tea and drink it straight away. And if the tea gets too cold, then you just add some hot water to the pot. Then I had a leisurely tea in England and now I'm forced to admit that there are times and places where tea cozys are appropriate.
Variations on the word "cozy" include: cosy, cosie, cozie and cozey.