This is the palm "flaring" its roots. This is common for many palms when they get older, especially Royals, Foxtails, Dates, even Queens will do it. Some Dates have 2-3 feet of solid root mass built under the trunk and exposed to the air. This also occurs if a palm experiences heavy moisture conditions, and wants to buffer itself from being flooded.

Thanks. Glad to know that's somewhat normal. We do get a lot of rain around here. I have a layer of pine bark mulch around the trees. Is there anything I can do to stop the flaring from getting worse?

baytopper....it sounds to me that the flaring is a good thing. You want the best underground root system you can grow. If you are worried about landscape looks, just pile more pine bark around to blend it in. I think as long as you have good drainage, your ok.