This quotation is found in Mere Morality by Lewis Smedes. Smedes is writing about the Sixth Commandment, and he claims that the meaning of this commandment extends far beyond simply not killing our fellow man. He says that it is rather a mandate to promote life:
We have not read its real demands unless we hear in it God's will to do all we can to protect our neighbor's human life and help it flourish. If we read the commandment as Jesus did, it becomes the law of life that gives flesh and blood to love.
So it is not enough, according to Smedes, for people simply to live and let live. We are obliged by God to help others, including the elderly, the poor, and children, who cannot subsist on their own. According to this version of Christian thought, all people are obligated to help other people simply because they exist. Of course, the limits of time, money, and other resources keep us from providing as much help as is needed for everyone, but the point is that the Sixth Commandment should underpin an ethos that respects and values every human life as much as one's own. It is an active, positive commandment according to Smedes, not just a negative prohibition against an immoral action.