I believe this quote means that government leaders often start out with good intentions for their people by giving them handouts and enacting laws (like mandatory seat belt laws) to protect them. But what often happens is that protection turns into control and control turns into totalitarianism...government has total control of all aspects of the people's lives and individuals are pushed down and silenced.
This is one of Huxley's main warnings, especially in his work, Brave New World. In this novel, the state tells its citizens who they can sleep with, what drugs to take, what jobs they can have, and what they can and can't read and do in their free time. Leaders say this world is good for the people, because they are protecting them from unhappiness by making sure there is no pain, or sin or social instability.
The only problem is, Bernard, John, and Helmholtz feel something is missing. They want some control over their lives, and seek to experience the totality of life...even the pain and mistakes....because only in this can one be unique and free.
It is the age-old debate over freedom or protection.