It's the shaft in the rear of the machine, that transmits the power from the trans out to the final drives. The final drives are the final gear reduction just before the sprockets (the big gear that drives the tracks).
so how do you tell if the cross shaft is out on it?
Also known as "bevel gear shaft" or "crown gear shaft".
Although on occasion it is possible to break one of these shafts (pretty severe loading) referring to the "cross shaft out" is more commonly in reference to having the cross shaft carrier bearings fail or be out of adjustment. Normally they should be preloaded with no allowable lateral movement which can be checked with prybar through cover plate access at the back of the case.
If they are loose it raises havoc with steering clutch operation, pinion gear to bevel gear mesh/backlash, and can lead to catastrophic failure.
On some tractors, you can actually feel the shaft movement through the steering clutch levers and can also contribute to why you can't get proper adjustment of the release mechanism.