Each primitive has an axis-aligned bounding cube. The hierarchical structure of the scene uses these cubes to create new bounding cubes at each internal node of the tree. These new cubes contain all of the children of the internal node. When a ray needs to be tested against the scene, it is only tested against a part of the tree if it intersects that part's bounding cube.
The image below is a balanced hierarchy of 16000 meshes, each with 26 faces. Meshes are expensive to test a ray against. The following statistics (computed for a non-antialiased version of the image below) show the benefits of the bounding volumes.
Anti-aliased rendering of scene with 16 sets of 1000 meshes (each mesh with 26 faces) -- 416000 total faces.