[archaeolept]

basically, if the size of your army exceeds the supply value of a province, the excess will be sprinkled w/ "hunger" which lowers morale and affects combat ability (as I recall). If an already hungry unit gets hit w/ hunger it will become diseased and gain an affliction.

human size troops use one supply. Giants 3. (generally, size of unit minus one, not counting commanders).

Magic items like bag of wine and cauldron of broth lower your supply demands, as do points of nature magic in commanders accompanying the force.

As well, supply is better near your castles