Acculturation is what happens when you live with French people for a while and start going "ooh la la" and eating snails. It means adopting the ways of a culture that isn't yours.
Acculturation is related to the word culture. Duh. Culture comes from a Latin word meaning, basically, farming. Now it refers to basically anything that people create and teach each other — singing, dancing, TV. Obviously people in different parts of the world have different cultures, and when they come together, the result is often acculturation. Picture a French guy drinking Coke and wearing a baseball cap and you get the idea.