This term is used when the center of a vehicle is caught on something (rocks, curb, sand, concrete) which causes the drive tires to be off of the ground. The vehicle is essentially stuck because it no longer has the ability to move itself off of the object it is center high on.
Vehicles (especially low to the ground cars) can become center high on sand if they follow the same path in the sand, digging the path deeper and causing a mound of sand to form in the middle making it possible for the front underside of the car to be lifted up and stuck in the sand while the drive tires spin uselessly.
Activites a vehicle can be center-high are mud-bogging/muddin' and other Redneck Games. Youths inexperienced to driving may get their vehicles stuck while offroading.