Keller wrote this book for a few reason, one of which is to the Christian so they can get off their butt and do good in this world and not just live in their own little Church bubble. Another reason Keller wrote this is kinda an apology (I mean that in the technical sense) to the non-Christian who may have bought into the new atheists that say religions, or Christians do not help the world.
Keller first sets out to explain what justice is, and how normally it is the poor who do not have an equal distribution to get, receive or enact justice. Pretty much, justice is to redistribute our resources to those who do not have them. This isn't just money, this is also could be education about money to those who are not good financial planners. This could mean giving those who do not understand the legal system, tools and knowledge on how to navigate that system, or giving away your extra clothes to people who do not have much, or teaching people how to use technology etc...
Keller took this argument from the puritan Jonathan Edwards, which I found surprising, as I thought the puritans were all about personal responsibility (right wing republicans) and not so much about systemic social issues (left wing democrats). On that divide, Keller shows that both parties are both right and both wrong. He looks at a third way in which we should see justice, which kinda takes the best from both worlds and paints a more realistic picture of the world.
If we think we do not own anyone else for our success, skills and knowledge then we really are not that smart. A lot of our opportunities like education, family, country we grew up that was political stable were things you did not choose or implement. It would be unfair (unjust) to treat those who did not have the same circumstance as you as inferior or to ignore them. Since you are equipped with success, skills and knowledge you should share that around.
Note that wasn't a religious argument, it was based on some sense of what is "right" or "fair" and what is "wrong" or "unjust". Most people would probably agree with this. Keller later on, when talking about doing justice in the public square shows why it is a good thing, and how Christians can probe their colleagues who are doing "good" things why they think what they are doing is "right". You don't have to be a Christian to hold to values of right and wrong, but sometimes, the underlying presuppositions are not considered why that is so. For example (this isn't in the book) it was the issue of abortion and human rights that turned the Raving Atheist to become the Raving Theist.
Keller gives a good Biblical taste of what justice looks like in the Bible and how the world shalom doesn't only just mean peace, but is about restoring the whole fabric of a community. Later Keller makes another point saying that Christians have more than the UN, Supreme Court or any other institution's definitions of human rights and justice to back up their case for the imperative of caring for people, and these issues can and should be discussed in the public square.
There is lots more in this book, so give it a read.
The first chapter of this book
9mark's review of this book
Another guys review of this book
Other books by Tim Keller I have read:
The Prodigal God
The Reason For God