The Collaborative International Dictionary of English v.0.48:

Clearance \Clear"ance\ (kl[=e]r"ans), n.
   1. The act of clearing; as, to make a thorough clearance.
      [1913 Webster]

   2. A certificate that a ship or vessel has been cleared at
      the customhouse; permission to sail.
      [1913 Webster]

            Every ship was subject to seizure for want of
            stamped clearances.                   --Durke
      [1913 Webster]

   3. Clear or net profit. --Trollope.
      [1913 Webster]

   4. (Mach.) The distance by which one object clears another,
      as the distance between the piston and cylinder head at
      the end of a stroke in a steam engine, or the least
      distance between the point of a cogwheel tooth and the
      bottom of a space between teeth of a wheel with which it
      engages.
      [1913 Webster]

   Clearance space (Steam engine), the space inclosed in one
      end of the cylinder, between the valve or valves and the
      piston, at the beginning of a stroke; waste room. It
      includes the space caused by the piston's clearance and
      the space in ports, passageways, etc. Its volume is often
      expressed as a certain proportion of the volume swept by
      the piston in a single stroke.
      [1913 Webster]

WordNet (r) 3.0 (2006):

clearance
    n 1: the distance by which one thing clears another; the space
         between them
    2: vertical space available to allow easy passage under
       something [syn: headroom, headway, clearance]
    3: permission to proceed; "the plane was given clearance to
       land"