When things stink, they smell terrible. If you throw food scraps in your kitchen trash can, it will eventually start to stink.
You can say that something stinks — your dog's breath, or your brother's feet — and you can call the offensive odor itself a stink. Figuratively, something can stink even if it doesn't literally smell bad: "I'm sorry, but that movie you recommended really stinks. It's awful." The Old English root is stincan, "emit a smell of any kind, or exhale."