A full count refers to a situation when there are three balls and two strikes on the batter. In this situation, the next pitch that is either a ball or a strike will end the at bat - with a base on balls or strikeout, respectively - although foul balls can prolong the at bat indefinitely.
A full count is considered a moment of increased tension, as neither the batter nor the pitcher have any margin of manoeuver left. The batter must swing at any pitch that is near the strike zone or risk being called out on strikes. The pitcher cannot waste a pitch, as it will result in a base on balls, but he cannot throw a pitch that is too easy either, as he knows the batter will be swinging.
Typically, on a full count, the baserunners will be running with the pitch, especially if there are two outs. This puts extra pressure on the fielders, and will often allow runners to either take an extra base on a base hit, or avoid being caught in a double play on a ground ball.
Also see: count