From The Collaborative International Dictionary of English v.0.48:
drawer \draw"er\, n.
1. One who, or that which, draws; as:
(a) One who draws liquor for guests; a waiter in a
taproom. --Shak.
(b) One who delineates or depicts; a draughtsman; as, a
good drawer.
(c) (Law) One who draws a bill of exchange or order for
payment; -- the correlative of drawee.
[1913 Webster]
2. That which is drawn; as:
(a) A sliding box or receptacle in a case, which is opened
by pulling or drawing out, and closed by pushing in.
(b) pl. An under-garment worn on the lower limbs.
[1913 Webster]
Chest of drawers. See under Chest.
[1913 Webster]