The power alleys are the sections of the field located between left and center field and between right and center field. They are thus named because they correspond to the area where power hitters will usually send balls that they hit "on the nose", i.e. with the most power.
The size of the power alleys vary significantly from one ballpark to another, depending on the configuration of the outfield fence. They can be as close as 350 feet from home plate (making the ballpark a bandbox) or as far as 400 feet or more in old-time parks (in which case home runs come at a premium, but outfielders must cover a lot of ground).
The distance of the power alleys are usually marked on the fence, just like those for the left and right field corners and for straightaway centerfield, given the importance of the number to determine how hitter-friendly a ballpark is.