The concept of supplies was introduced to limit the operating range of military units and make true supply lines a necessity for any sort of warfare.
Each SC/MC and squad has it's own supply level. SC/MC with manufacturing capacity can draw resources from your nation's pool and convert them to supplies. Those SCs/MCs will distribute supplies to other SCs/MCs, wich will distribute them to units.
The resources needed to make supplies will depened on average composition of your army. If you have 60% soldiers and 40% vehicles, the resources needed to make supplies will be 60% food and 40% fuel.
Raiding enemy SCs/MCs for resources will be possible, and useful mostly in Middle Ages-like times when lots of food supplies are needed.
When units run out of supplies, all engine-powered vehicles will be stuck in place, unable to move until they are resupplied (flying vehicles will be instantly lost). Other TOs and soldiers can move, but will randomly suffer "injuries" and losses over time. They will also have low morale and be generally less useful in combat.