Its an airtight container that you can fit in a semi-large pocket, which works as an ashtray, and you put cigarette butts in it.
In Japan, littering is extremely frowned upon, there are basically no public ashtrays, it is pretty common for smokers to stash their butts in these containers and then empty them out later.
Very different from the norm in much of the rest of the world where people just litter cig butts everywhere, toss them into garbage cans and start fires.
Seems like Metal Gear Solid is the gamer version of Disney's Snow White, because that girl motivated me so much to clean my room when I was a kid. Her and Mary Poppins. And so some extent, Pippi Longstocking too.