The peak is this point in the year because this is when water temperatures and (usually) upper level winds are at their most favorable for development out in the eastern Atlantic. Waters are also at or near their peak along the east coast of the US and Gulf of Mexico, allowing for close-in development from either tropical waves or occasionally along the tail end of a trough of low pressure (as we've seen recently).

In June and July, the waters and upper-level winds generally aren't favorable out in the E. Atlantic; ditto October and November. Conditions outside of the season are generally unfavorable in terms of both shear and upper-level winds with tropical waves both less numerous and less organized during those times.