Booking your trip during "shoulder season" usually means lower prices and fewer tourists, but can vary according to destinations. Here are some things to keep in mind...
Lower airfares will only apply if your whole trip is within that time period, however. So if you book your flight and part of it falls outside of a shoulder season, you will pay the higher price for the whole flight.
Pay attention to weather issues in certain areas. If you are going to the Caribbean, you will find emptier beaches and calmer weather...provided you are not traveling during hurricane season.
You may want to ask your resort when you book your stay if there will be construction. Often shoulder season is the best time for resorts to get all the repairs and remodeling finished.
Check the weather before you pack. And it never hurts to be prepared with a lightweight rain coat or umbrella.