What is apportionment and why is the census an important part of apportionment?

Apportionment basically means giving a fair share - dividing some resource in such a way that it's fair.

In politics, it means allotting so many votes to a state or district that every vote represents more or less the same number of people - otherwise some people's votes would be "stronger". Apportionment is used, among others, in the US house of representatives.

Census is important, because it provides a reliable information about the number of people in each district.