Just like the other International festivals that Epcot hosts there are food booths (or studios as Disney calls them) through out the World Showcase. Most of the dishes are prepared to be a treat for the both the eyes and the mouth. Grab a festival passport so you can check off everything you try. They are open daily from 11am until 9pm. Items on the menus marked with (GF) are gluten/wheat-friendly and (V) are vegetarian.
If you are on the Disney dining plan look for this symbol 
which means you can get that item as a snack credit.
Not all the booths shown but they are pictured in order of which you can find them starting in showcase plaza just before the Mexico pavilion and working your way around to Canada.
Up first is Decadent Delights in Showcase Plaza
Pop Eats! in Showcase Plaza
El Artista Hambriento “the hungry artist” in Mexico
The Painted Panda in China
Cuisine Classique in Germany
L’Arte di Mangiare “The Art of eating” in Italy
Takumi Table in Japan
Mosaic Canteen in Morocco
L’Art de la cuisine Francaise “the art of french cooking” in France
The Masterpiece Kitchen in Canada
The Deconstructed dish in Showcase Plaza
The International Festival of the Arts runs from January 12th until February 19th.