They have a great kids center with activities for all ages. Just make sure they attend the first day in order to meet other kid cruisers that they can do things with. There are so many other activities for the entire family, lots of shows and don't miss the ice show, everyone will enjoy that.
After cruising on the Allure of the Seas, I have to say they have the best kids' programs of all the ships we've been on in our 43 cruises. There is so much to keep them busy, it's amazing. Only problem, because the Oasis and the Allure are so popular, the prices are definitely higher than the Explorer, that's for sure.
With that said, we have found the Voyager-class ships (of which the Explorer is one) to be great for kids and they will have a wonderful time. Best way to find out all it has to offer is to go to their website; Welcome to Royal Caribbean International It's full of very good information.
__________________ 47 Cruises & Counting! Favorites: Paul Gauguin to Tahiti: Uniworld River Cruises in Europe; any of the Celebrity Solstice-class ships; Holland America for 12-nights in the Baltics & Russia; RCCL for 14-night Greek Isles, Turkey, & Croatia; Holland America for 14-day Alaska cruisetour; 10-night Canada/New England cruise; 21 days in Hawaii including a 7-night NCL cruise; Oceania for 25 days in Asia; & 3 months touring Europe by train. And many days spent in all-inclusive resorts!