To get your badge, you'll have to have general site access and rad worker training. Nothing major, and nothing too tough. However, you're entering the world of nuclear power, which special and unique, on top of the huge industrial facility you'll be working at.
So, to get in, you need to understand the basics of site safety, radiation safety, fitness for duty, etc.
That's what they meant by training. The background check is done at this point, but there is still the training to do. Don't sweat it, it isn't difficult..., but DO pay attention, it could save your life.
Good luck and welcome to the industry!
Justin