A bin is a specially made basket for certain stockpiles. A bin can be made from one wooden log at a carpenter's workshop or forged from 3 metal bars at a forge. Bins make it possible to store lots of objects into one tile of a stockpile. A stockpile without a bin will likely fill up fast, leaving any remaining items where they are to get in the way.
Bins are therefore incredibly useful to a maturing fortress. The best material for bins is generally wood, because wooden bins are the lightest bins and will therefore save time to your haulers. Of course, if you intend to use bins next to a volcano or something equally hot, you may want to use metal bins.
Stockpiles that use bins are ammo, armor, bars/blocks, cloth, coins, finished goods, gems, leather and weapons. Food stockpiles use barrels and large pots instead of bins. Other stockpiles do not use anything at all.
For information on managing bins in stockpiles, see using bins and barrels.