There can be significant benefits to traveling during a destination’s shoulder season. Prices tend to be lower than in high season and the weather tends to be better than in low season.
On the other hand, depending on the kind of trip you want to take, those benefits may not apply. For example, if you’re planning a ski vacation, you need snow—which means a spring trip probably won’t do. And if you’re looking to sunbathe on a sandy beach, autumn temperatures aren’t likely to allow for that.
If you’re just looking for a happy medium of some good prices (though maybe not the lowest), decent (though probably not perfect) weather, and slightly smaller (though not non-existent) crowds, shoulder season can be the ideal time to travel.