Logistics and supply are as important to armies as soldiers and weapons. They are also complex and laborious to manage, which is why Might & Fealty abstracts a lot of the supply management.
At its most simple, supply is what your soldiers eat (food) and where they get replacement equipment.
What you need to keep in mind is that in Might & Fealty, logistics are as important as battlefield strategy. Many games ignore this aspect of warfare, but many real campaigns were won or lost by the side with the better supply chains.
If the settlement owner has granted resupply permissions (see Permission system), and you are inside the settlement, troops can replace broken or lost equipment.
The amount of resupply available per day can be limited per permission list, with everyone on that list sharing the value. This value is in work-hours, and the amount of work-hours for each item can be found in the item descriptions. So if you want, for example, allow your vassals to take up to 10 spears a day out of storage, the value would be 300 because one spear takes 30 work-hours to produce. The reserve value works the same way and indicates the minimum amount of supply that has to remain in storage. So if you want at least 5 spears to be left for your own use at all times, set the reserve value to 150.
This abstraction to work-hours is one way in which the game simplifies supply. Instead of storing an amount available for each item, it stores available work-hours, which can then be turned into either axes or spears, for example. The soldiers screen lists the number of available items in brackets behind each entry. These are shared by building, so if you take out spears, the amount of axes also drops because the blacksmith produces both of them and if he makes spears, he can't at the same time make axes.
Camp followers (see below) automatically scavenge and barter for more supplies whenever you are in a settlement. If you have resupply permissions, they will be fairly effective at this. If you are not, they need to deal under-the-table and find shady dealers and will take much longer. Also, common items will be gathered much faster than high-level equipment.
Being able to resupply in a town is nice, but most equipment gets lost in the field, during battles. Having to travel to a nearby settlement for every replacement axe would dramatically hinder war efforts.
For this purpose, most armies are followed by a baggage train, in this game represented by the camp follower entourage type. For every camp follower you recruit, you can either set an equipment type or leave them to carry reserve food. This camp follower will attempt to acquire and maintain a supply of whatever you decide, with more expensive items being more difficult to acquire and keep. A camp follower focused on cloth armor will restock fairly quickly and can keep up to 15 of them in stock, while a camp follower set for horses will take a while to find a new one and can have at most 2 of them in reserve.
Of course, resupply is limited by local availability. A camp follower set for war horses will not magically acquire them unless there is a royal mews in the area where they can be found. Camp followers always gather from your current location.
Please note that whenever you change the assigned equipment type for a camp follower, any items of the old type that they had gathered are lost.
A planned feature is to allow remote resupply of equipment, simulating a baggage train bringing supplies from a unit's base to the unit in the field.
You can also replenish supply by Looting settlements. This goes much faster than friendly resupply and does not require permission, but it is a hostile action and it damages the local economy.
Looting is absolutely a viable part of warfare, and many armies in the real world would loot as they went, partly in order to replenish their supplies.