Nice, clear explanation, Pianodwarf.
So as Pianodward said, in the Senate, each state gets two representatives, regardless of the size or population of the state. In the House, the number of representatives is based on the population, and the most recent census numbers are used to determine how many representatives the state gets. States with more representatives have more power in the house.
But more importantly, (perhaps) is the fact that the number of congressional districts is equal to the number of electoral votes the state has in the presidential elections. As I'm sure you know, in the US, we don't elect presidents by popular vote. Instead, each state has a certain number of electoral votes, or points. If the majority of voters in that state select one candidate, then ALL of the electoral votes for that state go to that candidate. Sometimes a candidate (like George W) loses the popular vote, but gets a majority of electoral votes, and becomes president. That is why there was the big scandal about the state of Florida in 2000. http://en.wikipedia.org/wiki/United_States_presidential_election_in_Florida,_2000
The popular vote within the state was very very close, but when the decision was made that the majority of the votes counted went to George W, he got ALL of the state's electoral votes, and subsequently won the election.
So the census counts how many people live in each city, suburb and rural community in the country. Everyone who lives there counts, regardless of whether that person is a foreign student or an undocumented worker.
Arizona is an interesting case. The state has (or had in 2010)
one of the highest percentages of undocumented residents in the entire country.
And it is the presence of those undocumented immigrants, who were counted in the US census, that pushed the population numbers up and enabled Arizona to not only create a new congressional district and increase the state's power in congress, but also to increase the state's number of electoral votes.