they are used for removing bearings that have been pressed onto shafts. The splitter goes under the bearing to support it and then the shaft is pressed out using a a hydraulic press, or a screw puller or something like that.
Watch xtreme 4x4 today (Saturday). It should be a rerun of the FJ60/FJ Cruiser build up. I think Ian uses a bearing puller during a locker install in the FJ Cruiser.