I'm late, for a very important date.

What this quote is essentially saying is that in order for the machine to keep running the people running it must be machines themselves. If these people are always content, always happy, then that internal conflict no longer exists. When I was moving due to unpleasant circumstances I did not enjoy doing work. I didn't hate going to school, but it proved challenging for me to completely focus on homework. The proves similar for the people in the book. Those who are feeling unrest while work will not be as focused at doing their work. If The whole society is contempt though, this problem seems to utterly disappear.
They achieve this through the drug Soma, and through sexual promiscuity. "every one belongs to every one else," so the bonds that seem to binds us do not exist in their world. The analogy of a pipe is used to describe this. If a pipe has one hole then all the water rushes out the one hole with high pressure. If this figurative pipe has say 8 holes the pressure at which the water rushes out would be less and more distributed. Similarly, if a person binds themselves to one person their emotion pushes out with a high amount of pressure, where as if the are bonded to 8 the feelings for those people would be less pressured. I by the end of all of this the person is still feeling unhappy they can simply take Soma and have an altered state of happy reality. You are able to find contentment through different outlets, where as we must find reality through natural methods, (at least for those of us who do not abuse drugs, and even those people are not happy they are just a blithering mess). We do not have Soma, and promiscuity is frowned upon.
If I was given the choice I would not chose such a life. I am not always happy or content, but I am able to find my own happiness. I would chose to live in a monogamous relationship not just because it is socially acceptable, but because I personally want to find happiness in one person. I want to be attached to one person as apposed to eight, because even promiscuity would eventually lead to emotional unrest.