When Thomas Friedman uses the term “flat” in The World is Flat, what he means is something like “fair” or “providing everyone with an equal chance to succeed.” When he says that the world is flat, or is getting flatter, he does not mean this in a topographical sense. Instead, what he means is that the world is, economically speaking, becoming fairer. Our world has started to provide people from many different countries with an equal chance to get ahead economically.
In the United States, at least, we often use the metaphor of a sports field when we talk about economic competition. This might, for example, be a soccer field. Imagine playing soccer if one team had to run uphill while the other got to run downhill. This would not be at all fair to the team that had to run uphill. It would be a serious disadvantage. When competition is fair, we say that there is a level playing field. This field does not provide an advantage to either team. When Friedman talks about the world being flat, he is saying that the economic playing field has become level.
In the past, businesses in poor countries were, in essence, playing on a field that was not flat. They had to run uphill while their competitors in the rich world got to run downhill. In recent times, however, various changes have made the playing field flatter. He says that things like outsourcing, offshoring, and, most importantly, the boom in communications technology, have created a more level playing field where firms from more countries can actually compete on level terms. This is what he means when he says that the world is flat.
In this book, then, to be flat is to be fair and/or to provide everyone with an equal chance to compete economically.