Hi Patri, I would translate that as 'I've had a very active childhood'. Generally, when you say someone is active you mean it from a physical point of view, meaning they get involved in a lot of sports/dancing/etc as opposed to being sedentary :)
Also, if you are talking about traveling a lot you can also say 'I've had a childhood on the run/on the move' by which you mean that you were never rooted in one place and kept changing your location. Hope this helps!
Alex