The verb decompose means to break down or decay, like tree leaves that decompose into dirt, or cell phone batteries that decompose, resulting in more frequent charging for the user.
You know that the prefix de- means "remove" or "undo." And something that's composed is made up of parts. So to decompose is to undo all the parts until they go back to their original state: dirt. Living things decompose. When things like buildings or organizations break down, you typically use words like dismantle or deconstruct to describe the process.