A stash is, according WordNet's definition, a "a secret store of valuables or money".
The stash is one of the neatest features in Diablo II. The stash is a chest in the middle of the rogue encampment, and is reserved wholly for your use. You can store your items or gold in it. In Diablo II, the space in the chest was quite limited, but due to public pressure, in Diablo II: Lord of Destruction expansion set, the size of the stash was doubled. (I had the expansion CD from the beginning. Guess I was a spoiled brat.)
The stash is an interesting concept because it represents the concept of "home" in a game. In most of the CRPGs, the player needs to carry tons and tons of stuff, and has no single central point where to go - he or she is completely homeless, but needed by the Plot. In Diablo, you have a place where you can sit down and stuff your heaviest loot to the locked chest.
Even the more plotful games where the characters supposedly live somewhere don't have this kind of "home" system. I did notice that it is possible to create a home area of some sort using the Aurora Toolkit in NWN (though this needs some savegame and ITP file hackery so there's definitely no out-of-the-box solution for this...) and it's possible in games with wholly persistent worlds, of course.