The void of community
To a person born recently, community is whatever you make of it. You like some people, you dislike other people, leading to a map of friends that are a 'community.' Anderson focuses a tremendous amount of energy reminding the reader that for hundreds of thousands of years, that is not what community looked like. He says the human life changed drastically with the removal of the monarch from the public sphere, and when people stopped sharing religion amongst their immediate neighborhood or tribe. Community used to be a specific experience of the world that was shared with those who were nearby, but modern technology like cars has permanently changed that, leaving a void that can be filled with national citizenship, for instance.
The national myth
A nationalist in Anderson's view is someone who participates with a myth about national citizenship. He says that at its core, the nationalist myth is a shared fabrication, a social construct shared by enough people that there can be a feedback loop of approval so people commit their identities to ideas about citizenship that are plainly false. For instance, there are nationalists with emotional attachments to their country's role in global politics without any real research or facts.
Global tribalism
Nationalism is likened to other kinds of shared identity, which has some horrifying consequences. Anderson comments on the emergence of tribalism at the global scale, pointing out that if one nation has a national myth that contradicts the nationalism of another country, public opinion could spiral to the point of contempt and violence. People can easily use myths about what their country means to them to fight other people about what other people's country means to them.