Red Staplers provide a % bonus to the money you earn from each Floor.
When you burn or claim, it will take your Stapler bonus and add it to your next game, which will increase your production. You should normally, burn or claim, when you have double your previous Stapler bonus, as each time you start over, your bonus will be twice as big.
When you claim, you can get your Red Staplers and bonuses, without having to lose your Virus Installations, Upgrades, and Interns.
You will need at least 50 Red Staplers to Burn It for the first time.