Stopovers can be easily confused with connections, since both are preplanned stops in a flight, but there are a few points that distinguish them. A stopover is typically between 24 hours and five days, where you will have the chance to see a city that lies en route to your final destination rather than staying confined to the airport. This gives you the opportunity of enjoying a mini vacation inside of your trip, typically without incurring any further costs. With a connection, you would be departing on the next available flight. In a stopover, however, the flight leg for your end destination has been booked after this flight.
Stopovers are only available in the hub cities of a specific airline that are included in a typical flight plan. For example, if you're flying American Airlines from New York City to San Juan, Puerto Rico, you could book a stopover in Miami, Fla. at no extra cost, since it serves as a connection on certain flight plans, and enjoy a few days on South Beach. Many long-haul airlines, such as Singapore Air, routinely offer stopovers as an incentive to their customers, yet many U.S.-based carriers limit them to their rewards programs.
Staying past five days will most likely be viewed as one completed leg of a flight journey and won't qualify as a stopover. It will always be best to check with your airline while booking to see of any specific rules, restrictions or fees that it may apply.