What it says right on the tin!

Break down your old and/or unused armors into something somewhat useable.  Current rate is roughly half of what it takes to make a new armor of the respective recycle.  For Scale and Plate, you'll lose the chain, but still get some of the leather.  But hey, its better than just throwing it in a lake or sticking it in storage forever.

To break down metal armors you need a chisel and hammer, and cloth you just need shears.

Some numbers to bite into:
(These arent comprehensive, but just examples)

Tailored Gambeson Body
Cost: 10 Bolts of Cloth
Recycles into -> 4 bolts and 8 flax twine

Scale Body
Cost: 6 Scales, 11 Chain, 14 Leather
Recycles into -> 3 Scales, 0 Chain, 5 Leather