Slow food is a movement that advocates food raised and prepared in a healthier, more natural way. That means an emphasis on foods that are natural to your local region.
The slow food movement was founded in 1986 by an Italian man named Carlo Petrini, growing out of a protest that aimed to stop the McDonalds food chain from opening an outlet near a historic site in Rome. Wikipedia has a good writeup on the Slow Food movement.
SlowFood USA gives the description of "a global, grassroots movement with thousands of members around the world that links the pleasure of food with a commitment to community and the environment."