This is a baseball phrase used to describe an inning in which no batter reaches base. It is an unofficial term and carries no significance in the record books. A perfect inning will typically be the result of quality pitching and more often than not, three strikeouts. Although certainly helpful in helping a team win, a perfect inning usually has no effect on the rest of the game unless the pitcher begins to combine the perfect innings together.
The phrase is a derivative of "perfect game," which is when a pitcher has nine perfect innings in a row. If a pitcher manages to pitch one perfect inning, especially the first, players, announcers, and fans will not mention the fact due to superstition. Many believe that mentioning a perfect game before it has completed will hurt the pitchers chances of making it happen. However, if the pitcher has already allowed a player on base or a hit, mentioned a perfect inning is considered acceptable.