Bounding volumes are used in many components of three.js. If you properly setup a geometry (e.g. by defining a position attribute), bounding volumes can be automatically computed by the engine.
BufferGeometry.boundingSphere is used for view frustum culling. If the bounding sphere is not yet defined, the logic will perform the computation, see:
The bounding sphere is also computed automatically when doing raycasting. The bounding box is optional. If you define it, the raycasting logic will test it too before doing the more expensive ray/triangle intersection tests.
BTW: The docs do not explain these details since they are somewhat internal stuff. Especially since the bounding sphere is automatically computed. If this does not work in your app, you might have problems with your geometry setup.