The quotation comes from a collection of essays called Resistance, Rebellion, and Death. What Camus is driving at here is the notion that freedom isn't something that's given to you or something that's your right as a human being. Rather, it's something to be worked for and fought for as part of a lifelong struggle.
This inevitably puts the onus for the attainment of freedom squarely on the shoulders of the individual. It is his or her responsibility to see that they achieve freedom for themselves and for others. In is only when we recognize this responsibility, this overriding sense of duty, that we can join together with others to engage in the wider political struggle for freedom in society. Camus sees this struggle as primarily concerned with the rejection of the humiliation to which the lower orders of society have been subject for centuries.