Correspondence refers to the IotM-granted bonus of one free item per day via kmail (but from the game itself and not another player). If you've unlocked multiple correspondents on your account, you can choose between them in the Eudora tab of the Options menu.
Currently, KoL features these correspondence items:
- My Own Pen Pal kit
- GameInformPowerDailyPro subscription card
- Xi Receiver Unit
- New-You Club Membership Form