Sometimes when I see an ad or a webpage on something, it makes me start wondering. This happened earlier related to seeing a site that can make a custom rubber stamp. I started thinking about the term itself to figure out where it came from. It seems that historically it came from the practice of subordinate employees or officials being deputized and given the authority to sign the name of their superior or employer. I used to do this when I was an administrative assistant, but I would sign my initials so that it was known I had signed it on his behalf.
Then in some cases a literal rubber stamp of the signature was created, this also happens frequently with elected officials, they don't sit there and sign the many documents and letters, they or someone in their office "rubber stamps" it. There's a deeper meaning of the term "rubber stamping" though where it's meant to suggest an endorsement took place without careful thought.