What have been the main political drivers of globalization in the last 20 years?
Globalization is the shrinking and removal of economic boundaries between countries. Free Trade is one example, where the countries in a free trade agreement agree not to charge tariffs (taxes) on imports from the other country. So cattle grown in America could be sold at the same price as cattle grown in South korea, for example, or cars made in Mexico could be sold with no extra taxes to compete with cars made in the United States.
The effect of this is that the prices for manufactured goods tend to go down in those countries, but that jobs tend to move from the more industrially advanced nation to the less developed one. Labor costs are cheaper in Mexico so it makes more sense as a business to move the factory there, which costs America jobs, but lowers the prices of vehicles.
The main political driver is business influence over politicians and elections. Businesses, especially corporations, donate money to candidates who are pro-free trade, and thus influence the passage of NAFTA and the recent agreements with South Korea, Colombia and Costa Rica.