The luggage is trucked to the resort seperately. It can take several hours before you are reunited w/your luggage again, so bring anything necessary (like swim stuff or pjs in your carryon).
I think when you check in at ME they ask how many pieces and may enter your baggage claim #'s (can't remember). We have always had excellent luck w/ME and I am so glad we don't have to struggle through the airport w/kids, strollers and luggage!
A great tip I picked up here is to pack a little bit of everyone's stuff in your suitcases, that way if one goes missing, everyone is still all set. However, I think they will help you track down and deliver missing pieces, but it will never be clear if the case was missing from the airline or mishandled at ME.
If you are very concerned about it, don't put the ME tags on your luggage and retrieve them from baggage and just bring them to the buses yourself.