"The axial body is that portion that is directly attached to the spine, including the head, ribcage, and pelvis. "
Presumably, axial onset is when the muscles of the trunk are the first part of the body to be affected (as oppossed to upper or lower limb onset, or bulbar onset). As with other types of onset, symptoms would vary depending on upper or lower motor neuron involvement, degree of progression and so on.
Someone may wish to correct me. Dani