It just means one is after another.
It means you were running 3 weeks in a row. One right after the other. You ran one week, then you ran another week without stopping, then you ran another week.
Another example of this "back to back" phrase is when you're watching TV.
If they are having many episodes of a show played one after another, the episodes of that show are "back to back". It would NOT be back to back if you had one episode of that show, one episode of a different show, and then one episode of the first show. It has to be the same thing, one after the other.