A connecting flight from your destination is when there are no direct flights or need to stop and reach their final destination, as a matter of routes, the airline and different factors.
Direct flights are more expensive, and a good option is to find different routes and flight will be cheaper, but takes more time on the trip.
On your ticket will indicate how many connections have your trip, connecting flights are classified according to the airline, shipping information, check-out and sometimes the seat.
In general, calculate the time that passengers need to make your flight connection or change of airline. To allow transhipment and finalize the time in case there are flight delays or a change in schedules.
Normally do not have to re-register at the airport if you travel only in transit, but if you need to carry your papers in order to make your trip more enjoyable.
Example: going to travel to Australia from Cancun, but the flight made stops in Mexico City and Los Angeles (YES, you required USA visa) even if your flight is traffic only and make your connection in Los Angeles.
The airline will let you know , if you do not have USA visa how to change the route and they suggest you other options for not to suffer setbacks.
In case you lose your connection, it depends if booking your flight on one airline or different companies, if everything is on one airline, you can assign the next flight, but they are different companies have to fix you to reach your final destination.