This is what America's Test Kitchen (sorry, paywalled) has to say about it:
Sometimes baked potatoes can use a flavor boost. And instead of light and fluffy, most often they are dense and crumbly. We found that baking the potatoes on a bed of salt remedied these problems. Moisture that escaped the potatoes during baking was trapped in the enclosed pan, absorbed by the salt, and eventually reabsorbed by the potatoes, making their skins tender and their flesh light and fluffy. All we needed to do was fine-tune the variables. Using a hot oven and uncovering the potatoes toward the end of cooking ensured dry, crisp skin. A 13 by 9-inch baking dish provided plenty of space so that we didn’t have to crowd the potatoes, and 2 1/2 cups of salt allowed us to thoroughly cover the bottom of the pan.
I have found that salt roasting potatoes makes the skin crispy, without it getting hard. Like the above says, the potato itself seems fluffier. The way the salt seasons the potato is particularly nice as well. Incidentally, you can reuse the salt over and over again, so it's not as wasteful as it might seem when you first consider the method. You'll want to keep separate salt for things like this, though, since it picks up potato flakes and discolors a bit.
EDIT The ATK method calls for covering the 9X13 baking dish (for 4 potatoes and 2 1/2 cups of salt) tightly with aluminum foil and roasting at 450F (232C) for 1 1/4 hours. Remove foil, brush potatoes with oil, raise oven temp to 500F (260C) and continue roasting for 10-20 minutes, until potatoes are tender when pierced with a knife and the skins are glossy.