A BSP tree progressively subdivides the space using planes which are the nodes of the tree. At some point we stop subdividing and everything in the remaining space is part of a 'leaf' which contains a number of polygons. Typically we traverse the tree to locate the leaf in which a point in space is (say the camera origin) and work from there. A second structure, the Potentially Visible Set, tells us which other leaves can been seen from this leaf, and we test their bounding boxes against the camera frustum to see which we need to draw. Leaves are also a good place to start for collision detection since they divide the level into discrete areas for testing.
This BSP and PVS technique has been made famous by engines such as Quake and Unreal. Ogre provides support for loading Quake3 level files to populate your world through this class, by calling the BspSceneManager.LoadWorldGeometry. Note that this interface is made available at the top level of the SceneManager class so you don't have to write your code specifically for this class - just call Root::getSceneManager passing a SceneType of ST_INDOOR and in the current implementation you will get a BspSceneManager silently disguised as a standard SceneManager.