To apportion is to divide something into shares and hand it out. With 11 guests at your birthday party, it makes sense to cut the cake into 12 slices and apportion one to each — leaving one slice for you!
The verb apportion means "allocate" or "divvy up," and it's often used to talk about the way money is distributed. For example, your parents might evenly apportion an allowance to each of their children, or apportion slightly less money to your youngest sibling. In government, power is also apportioned in various ways, as when laws apportion a certain number of congressional representatives to each state.