It means exactly what it says: do not push...with a loader or some other heavy equipment.
If a dump truck is working off-road somewhere (which they do a lot) there's a chance they could get stuck in mud. Or, they could be stuck at the bottom of a hill. (both of these things happen often. Sometimes simultaneously. My family's full of truck drivers, and almost all of our work is completely off-road). Tow trucks that can tow full size trucks are expensive, so if you've got a loader lying around, it can be tempting to use the loader's bucket to, literally, push the truck from behind out of trouble (obviously, given the engine, windshield, etc. you can't push it from the front). However, this can actually break the dumping mechanism on the truck.
So, to get a truck out of trouble, you have to hook a chain onto both it the loader, and then use the loader to pull the truck, instead of pushing it.
