Back when typewriters were in common use and photocopiers were rare, one kind of paper you used to be able to buy actually came as two or more sheets stuck together at the top with carbon paper between each sheet. This way you automatically had multiple copies of whatever you put on the paper. This was commonly used to save typing work for office memos, but was especially common for forms. If they were filled out by hand, they'd put instructions on the top of the first page to "press firmly when writing" to ensure even the bottom copy was legible. I think such forms are still around in some places, but they now use specially backed paper instead of separate sheets of carbon paper. Forms also typically had different words at the bottom of the carbon copy pages saying who got that copy.

Now the "blind carbon copy" I always thought was an email innovation. However, Unreason in the comments below found a reference to it from a secretarial handbook from 1979. Wikipedia explains it was made to emulate an old office typist trick of adding addressees to one (or more) of the carbon-copied sheets after the copies were made, so that the others don't see that addressee. According to the handbook, secretaries were supposed to make note of these extra recipients in a file, but the other recipients would be "blind" to the fact that these extra people received copies.