Early is 11AM. You never know for sure when they will start to let you board. Normally boarding starts by 12 noon but it could be earlier of later depending on how disembarkation went with the previous cruise.
If you want to get on early as possible be there by 10:30 or 11. You will most likely have to wait to board but once they open up the ship to boarding you will get on. Some people don't like to wait and don't arrive until 1PM, but it seems that no matter what you do you will end up at some point waiting in line to board. My perspective is - I'd much rather wait at the ship and possibly get on early than wait at a hotel room or airport and arrive at 1PM.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013