The outer curved shape looks like it is made of multiple paths, not one single closed path. A closed path is one which is closed at the ends, forming a single path to make a completely enclosed shape. That is probably why you are getting an unexpected result.
See the Adobe Help page here to help you understand the difference between closed and open paths, which is a key concept in vector image editing.
So, anyway . . .
Do it like this instead: draw the outer shape as a single closed path (use the Pen Tool). Make sure the lines you want to use to divide the shape with are overlapping.
Select all, and hit the Divide button in the Pathfinder.
Finally ungroup, and and you will get individual pieces, each one is a closed path.