We just got off the Glory yesterday. We have been on 16 Carnival cruises, so we are " Platinum ".
It's pretty much as SandyBeach said. There is a private room for check in. a special place at the pursers desk for platinum members, so you don't have to wait in the lines, priority tendering, etc. The biggest thing was disembarkation. The last night we were given special platinum colored luggage tags and a letter stating to meet in the main lobby no later than 7: 10 a.m.
They had a section set aside for platinum members and after about a 20 minute wait, a crew person came and got us and away we went. Downstairs, the luggage was in a special place which made it so easy to find. I spotted mine before we were even down the stairs. We were in the car and on the way by 7: 50 a.m.
Even if there were no other perks, that alone would be enough.