It represents the people, but in a horrible proportion unlike the house. In what world does that make sense?
The Senate makes sense in this http://www.thisamericanlife.or... world (summary: a city where the majority of the people want to send their children to private school, so they actively sabotage the public school system).
For a law to get passed the majority of people have to agree upon it (the House), and the majority of different kinds of people have to agree upon it (the Senate). So what the Senate does is protect the minority. Ideally there might be some way to repurpose the Senate to be based on race or socio-economic situation, but I don't now how realistic that would be to implement. So the Senate is based on geographic location. Texans are different than Californians which are different than New Jersians, etc. I realize it's not ideal for every possible representation for every "kind" of person, but it is something.
In the first few decades after the American Revolution, there were some bad examples of a 51% majority abusing the 49% minority. So the idea of a bicameral legislation was created to be a forcing function to prevent the current 51% majority from creating abusive laws.