This is a slang phrase used in baseball which refers to the central, vertical axis of home plate. It is used in reference to pitching, whereby a pitcher throws the ball down the middle of the plate. This is a very dangerous place for a pitcher to throw it if they cannot throw fast enough to get it by the batter. As a result of its susceptibility to big hits, the center of the plate is known as the heart. It is mainly used by commentators and fans and is not used in any technical description of a pitch.
An example of usage of this phrase is, "Since he threw it down the heart of the plate, I knew I could hit it out of the park." The center of the plate is positioned on the field in such a way that a pitch thrown down this path, if hit with a good swing, would contact the sweet spot of the bat. Despite the risk, many pitchers who are capable of throwing very fast routinely throw balls down the middle of the plate. Nolan Ryan, a Hall-of-Fame pitcher, is famous for throwing fastballs down the center of the plate, sometimes to taunt batters and showcase how fast he could throw.