In the image below, you'll see that tropical storms generally form in the western Caribbean, then travel north/northeast into the Gulf of Mexico during the month of June.
By July, storms are forming more in the eastern Caribbean, traveling northwest into the Gulf of Mexico or along and off of the Atlantic Coast.
Hurricane activity really begins to pick up in August and peaks in mid-September. Tropical storms are now forming from waves off the African Coast. The storms travel due west into the Caribbean, Gulf of Mexico, and Atlantic.
September is similar to August, except more storms are forming. Heads up if you've got a cruise planned.
October can still be a busy tropical month. Storms tend to form back in the western Caribbean and up through the western Atlantic over the still warm tropical waters.
By November the Hurricane Season (June 1st - November 30th) is winding down. Storms tend to form in the still warm western Caribbean.