Specialist Firm
  
Basically, a company that employs specialists. But not just any specialists (a firm that employs Space Shuttle Payload Specialists isn't what we'd refer to here as a "specialist firm"). These specialists have to do with the stock market.
The NYSE uses specialists to maintain market liquidity for the stocks that trade on its exchange. Each specialist has a stock they're responsible for. They act as middlemen for transactions, facilitating the buying and selling of shares.
The specialists also hold a certain amount of shares in reserve (an inventory maintained by the specialist) to use when the buy side or sell side get a little skimpy. If there aren't enough people on a certain side of the transaction (not enough buyers or not enough sellers), the specialist will dip into its shares to keep the market humming.