Stash is a storage place for all kinds of items, vests and weapons like duplicates of rare weapons, weapons which can not be used currently due to their higher XP requirement, various support equipment like medkits, explosives like C4, etc. and all other stuff that can be picked up at some later stage, if and when needed. It's wise to place some extra equipment into the stash for a later use, in the event that you are not close to an armory but near to a stash. Items that you have stored to the Stash are saved and can be accessed through every stash within a map and are also available between rounds in a Singleplayer campaign or Online invasion.
A stash can contain a maximum of 255 items in total but only 120 different types of items are shown.
The content of the stash is server specific and not carried over between servers unless you play on an official invasion server, which share the profiles (and saved items) between each other.
Some Stashes are near armories while some other are located near the bases where there are no armories.