His basic thesis is that the "Jewish people" is not a long-standing, distinct nation or ethnic group, exiled from its homeland and now returning, but a diverse group of people of varying nationalities united by their religion. The concept of the Jewish nation was, on his reading, created by the Zionists from the mid 19th century onwards in the context of the rise of "nationalist" ethnic histories around the world and most particularly in Europe.
I'm not in any way qualified to assess his arguments, but I certainly found them compelling. At risk of oversimplification, let me summarise.
1. The early stories of Israeli history as presented in the Bible - the story of Abraham and the patriarchs, the Exodus and the kingdoms of David and Solomon - are largely mythical accounts with little supporting archaeological evidence.
2. The large Jewish communities present throughout the Roman empire, the Middle East, Central Asia and Eastern Europe were made up largely of converts, with Judaism active in the task of conversion from the second century BCE until the 4th century CE in the Mediterranean and longer in the Middle East and Central Asia. The European Jews were largely descendents of these converts, not of ethnic natives of Judea.
3. There was no historical exile. None of the major conquests of Judea - the Babylonian conquest, the Roman quashing of Jewish rebellions in 70 and 135 CE, the Arab invasion of the 7th Century - resulted in mass expulsion although in some the urban or military elites were expelled or taken captive. This means that the pre-1947 inhabitants of Palestine were in part descended from the original Judean population, although of course mixed with various waves of immigrants.
Of course this argument undercuts the basic justification for the Jewish "return" - that they are reclaiming their ancient homeland. However, his purpose is not to advocate the dismantling of the nation of Israel. Instead, he is asking his fellow Jews to see their nation differently. At both the beginning and end of the book, he shows his hand as a strong advocate for liberal democracy, defined as a state in which all the people are equal and sovereign irrespective of their race or religion. Israel, he says, is not currently a true liberal democracy because it is constitutionally established as a "Jewish state". Jewish people (including those who have never lived in or even been to Israel) have privileges not available to other residents including those who are Arab, Muslim or Christian, even if these "others" have lived in the land all their lives. He sees in this distinction a time-bomb waiting to destroy Israel from within.
Naturally this book is controversial in Israel and worldwide. There's a war on, and this heightens emotions on all sides. Furthermore, a lot of people have invested themselves emotionally in the Jewish identity of Israel, including a lot of Christians. Yet aside from the importance of its questions for Israel, it asks us a broader question. As humans, are we willing to embrace an inclusive identity? Are we able to say "you and I are one people" even if we have different skin colour, speak different languages and have different religions? This is an ideal that humans have rarely attained, but our survival in a heavily populated world overburdened with weaponry may depend on us keeping on trying.