Dans le wagon où nous nous asseyons d’habitude, il y a de plus en plus de monde le vendredi soir.

Because où is the relative pronoun used for place in French. Here it means where:

• le wagon où nous nous asseyons = the carriage where we sit
• More natural English might be the carriage we usually sit in

French uses où after a place noun much more directly than English does.

You could also say something with dans lequel, but où is simpler and more natural here.

They do two different jobs:

• the first nous = the subject pronoun, we
• the second nous = the reflexive pronoun, ourselves

The verb is s’asseoir, a reflexive verb meaning to sit down / to take a seat.

So:

• nous nous asseyons = we sit down / we take our seats

French often uses a reflexive structure where English does not.