There are a lot of different stews you can make, some of which are very useful in many ways, but only one will unlock the puzzle. You can see recipes for all of the stews in this post in the VV2 guides section.
There are two puzzles that involve stew. The first stew-related puzzle is solved the first time you successfully perform all of the steps needed to make a stew that the villagers can eat. The second one requires a villager to use a specific stew to solve the puzzle.