The Collaborative International Dictionary of English v.0.48:

Hitter \Hit"ter\, n.
   1. One who hits or strikes; as, a hard hitter.
      [1913 Webster]

   2. (Baseball) The batter; as, there are two strikes on the
      hitter.
      [PJC]

   heavy hitter

   1. A baseball player who gets many extra-base hits.

   2. A person who is very important or is very effective at his
      profession.
      [PJC]

WordNet (r) 3.0 (2006):

heavy hitter
    n 1: an influential person who works hard to promote the causes
         they are interested in