The obvious advantage is that you have your own little house. You also get this with a caravan - plus you have a car - but of course caravans are more difficult to travel around with, and to manage when you get to a site. You can use a motorhome as a car as well - it's a little inconvenient but perfectly possible - or have a bike on the back for quick transport.
You also save a lot of money as you can cook for yourself, and unlike with renting an apartment, for example, you can move on as much as you like. This may be the biggest advantage - if you don't like the place you are staying, or you want to go somewhere with better weather etc, you can just leave - even if you have paid site fees, they usually aren't too high, nothing like as expensive as cancelling an apartment or hotel stay.