Apportionment is distribution in line with an agreement, plan, or strategy. In the context of the law, U.S. congressmen are apportioned to the House of Representatives according to their state's population. Apportionment can also refer to liability being distributed to a number of individuals or groups in a court case. In short, an apportionment can be described as a part of something. If you have a whole pie and there are four people, you would cut it into fourths. Those fourths would be the apportionment for each person.
Many times, the result of civil lawsuits is that a defendant or multiple defendants will have to pay damages to the plaintiff. If there is more than one defendant who is ordered to pay damages, then the amount of damages can be apportioned according to liability, So, for example, if one defendant was found to have 3/4 of the liability, then 3/4 of the damages responsibility could be apportioned to that defendant. The other defendant would have the rest of the damages apportioned.