My pediatrician says my child may have compression neuropathies, but I don't understand. What does it mean?

Nerve pressure. Compression is the same thing as pressure. The medical term refers to problems with nerves (numbness, tingling, weakness, pain) caused by something pushing on those nerves. The something can be bone, ligament, muscle or other soft tissue.
See below. Compression neuropathies are anatomic points in the body where there is too much pressure on a peripheral nerve. An example would be carpal tunnel syndrome. The more important question to ask is why a child has this problem and should be completely worked up by the pediatrician or neurologist.