After the briefing in the guerrilla base you (and your subordinates) are given a default/recommended load-out for the following mission.
If you already have a weapon suitable for the upcoming mission (decided by your leads ;) stored in the boxes it will be given to you. If you don't, you may receive a new one.
Similarly the subordinates you'll start the following mission with - they get their weapons from your ammo-boxes.
You can always change your own load-out using the ammo-boxes prior to going to the Assembly point.
(!) You can adjust your own load-out & also the load-out of your subordinates in the Team Inventory in the Map Briefing in the beginning of the actual mission (after it's been loaded).
You will find it in TEAM tab, under each character's details ([Inventory])
Load-out you have on the guerrilla camp prior to each briefing is not taken directly to any of the main missions, but you'll take what you currently have with you if you leave the camp for some lone-wolf Scouting.
What you bring back from the Scouting, or what you or your subordinates bring from any of the missions, will be stored in the ammo-boxes (or briefing Team Inventory) even if you throw it in the camp on the ground (the guerrillas care for each other's equipment ;)
There are last few remaining bugs (fixed in the 1st patch) when an unit outside of your team will get his hands on your weapons and items you have stored ;)
Please note, that uniforms, helmets, vests, backpacks and items (GPS, map, NVGs...) are not (currently) stored in Kerry's own possession.