Since we are limited to short answers here, I will give you a brief summary of Waltz's main point only...
The title of this book says it all, really. Waltz is a realist. This means that he believes that the major fact of international relations is the fact that the international order is anarchic. What this means to him is that the world has no ruler that can force countries to do anything the way a country's government can force its citizens to do things.
Because of this, countries are most concerned with keeping themselves secure. They will always act in ways that are meant to increase their own security (as opposed to acting in ways that are based on morality or political ideology).