I read the introduction of the wiki article, but I'm still at a lost.. the third party pays back the broker because it "wants to influence how the broker routes client orders" what? so if I were the broker I would deny or allow my customers transactions based on a third party?

I'm sure is not like this and the broker won't deny any transaction if I were the broker I would just get a commission on some transactions by third parties but I don't see what I could change in order to get a greater commission.

could you elaborate please, I'm at a lost.