Basically, they're asking to not be slammed by a hurricane or, if it has to happen, the back-up is a prayer that it's not too devastating. Now, hurricane season lasts until the end of October when the locals observe their Thanksgiving, which is another holiday to be thankful the islands made it through another year. This year is supposed to be pretty brutal. Predictions say hurricanes will be stronger and occur more often. But Hurricane Supplication Day is more about keeping spirits up.
Nobody wants a storm to strike, but if one does, it helps to be in a good frame of mind.
For tourists to get involved, and given the stakes, it's not a bad idea, you can go to any church or gathering of locals. You know, it's the islands, and everyone's pretty friendly.