Different areas of skin send signals to the brain via spinal nerves that come off the spine at different parts of the spine. These are called dermatomes. These give us an idea of what functions will be controlled so lower leg function are controlled by nerves comming off the lumbar spinal cord. The spine is composed of vertebral bones and there are regions called the cervical, thoraacic, lumbar and sacral vertebra. The cervival vertebra are in the neck and these control the arms. A broken neck around C3 (third cervical vertebra) is going to cause quadraplegia because all nerve signals below the point on C3 and below are lost. So any thing in blue green and red and orange are affected. Now if the break is say at L1 (first lumbar vertebra) then the functions below that i.e. L2-L5 and S1-S5 are lost so the orange and red function is lost and the blue and green functions are fine so this person would be paraplegic and their legs would be affected.
So the blue bars below are nerves that are firing at the level of the arm there are 14 nerves firing (in blue) at the level of the legs 14 nerves are firing.
In MS the lesions can be anywhere in the spinal and the things they affect will affect the symptom that develops. However you have to imagine that the if there are random lesions in the spine then the chances that the pathways to the legs are affected will be much higher than the arms. So in the example below at the level of the arms 5/14 nerves are blocked but at the level of the legs 12/14 are blocked.
This is why movement in legs are more affected than arms. The peripheral nerves in the leg are fine but it is the signalling in the brain and spinal cord that is affected.