To reapportion is to hand out or deliver something in a new way or at a different time. Your teacher might reapportion the math quizzes after realizing the pages weren't all printed on both sides.
When you reapportion the candy from a piñata among birthday party guests, you take back what they've grabbed and then parcel it out, making sure each child gets the same amount. When Congress reapportions voting districts, it rearranges them and assigns citizens new polling places. To apportion is to assign a part of something, from the Latin portionem, "share or part."