Concurrent jurisdiction is when your claim could be in more than one workers’ compensation system (or court) at the same time. No systems allow you to collect benefits twice for the same thing, but sometimes you can “pick and choose” the best of both systems. So if you have a Longshore claim because you were hurt in the State of Maine or New Hampshire (or any of many other states), but were hurt in a maritime occupation with enough connection to the water, you might be able to get benefits under one system or the other that you would not if you were in one system alone.
You should not have to worry too much about concurrent jurisdiction, but you should be aware of it and should ask your attorney if your case might benefit from concurrent jurisdiction in one or more workers’ compensation systems.