A rubber stamp is a negative engraving, made of rubber or other resilient substance, which is used to mark paper or other documents with ink in a quick and consistent fashion. The stamp is first inked by applying it to an inkpad, and then pressed against the document or surface to be stamped - leaving an image of the stamp in ink. The rubber stamp produced a noticeable improvement in the speed of office paperwork - and, some will say, produced a noticeable increase in the amount of office paperwork, as the work expanded to fill the available time.
In modern slang, rubber stamp is used as both a noun and a verb. As the original invention of the rubber stamp made the act of approving or denying paper requests easy and fast ("bang the stamp on the ink pad, bang it on the document, and there you are sir, stamped. Same every time."), the rubber stamp came to be used as a symbol of symbolic action - that is, the act of stamping occurred at the expense of any actual oversight.
So, in modern times, when a body or an officer 'rubber stamps' something, it means they have moved it past their stage of approval or denial quickly, and the implication is that they've done so without actually doing the requisite oversight work. That's the verb use. The noun, in slang, simply means an office, official, or part of the bureaucracy that is known for its incuriousness and quick passage without oversight.