Globalization is the process where the economies of various countries in the world become more and more connected to one another. In a globalized economy, people from one country can buy goods quite easily from other countries. Nowadays, people in one country can even buy services from other countries (because of the internet a company can have accountants in India, for example, do its taxes).
The main advantage (economists say) is that people get more goods and services for a cheaper price. Instead of having to buy something made in America, I can buy the same thing made in China, but cheaper. That's good for me. You can also say globalization helps countries like China get richer and eventually that will mean they'll buy more stuff from us (like computer programs and movies and such).
The disadvantage that most people see is that this means just about any job (in a rich country like ours) can end up getting sent to another country. So we have to compete with people who have way lower standards of living and can work for way less pay. This really annoys a lot of people in the US and that's why we have a lot of calls for less in the way of free trade.