The time between connecting flights
It is desirable to have long layovers if you wish to visit the local area. It is desirable to have a short layover if you just want to get on with your trip.
On international flights, it is a good idea to have a minimum of one hour layovers, to pass through any possible security checks and to have your baggage transferred to the next plane properly. It is not a Good ThingTM if your baggage misses the connecting flight.
About the worst thing that can happen during a layover is the airport stopping departures because of weather or some other reason. This is even worse at international layovers, since that means you are pretty much stuck at the airport until you can leave. Consider being prepared for this possibility for locations that are frequently snowed in or get adverse weather.
During layovers too short to leave the airport, but too long to just wait, it's usually a good idea to have reading material or a music device. It's also a good oppurtunity to use the bathroom since airplane bathrooms aren't too much fun. There are also usually shops where you can get some food, since airplane food isn't too much fun, either.