Hurricanes seem to happen mainly in September and October. Why is that?
Hurricanes (and tropical cyclones in general) are most numerous during the late summer and early autumn, but not as much in October (when their activity usually tends to lessen). The peak of activity is generally in the late August-early September period.
That is the time of year when the two most important ingredients for the development of hurricanes and tropical cyclones occur. Those ingredients are warm ocean water: 80 degrees or higher; and weak vertical wind shear (no or little change in wind direction and/or speed with height).
This is also the time of year with the greatest frequency of westward-moving weather disturbances in the tropical and north-tropical North Atlantic Ocean that can eventually develop into hurricanes. Water has a relatively high specific heat (the heat required to raise its temperature) and is therefore rather slow to warm up. Tropical oceans in the Northern Hemisphere usually reach their warmest temperature in late August and early September, several weeks after the time of year of strongest heating by the sun (the latter portion of June).