That's a friend that you are corresponding with. This is an old term used before the internet and modern technology because you communicated with a "pen", you wrote to each other.

In the days that people wrote letters and mailed them at the Post office, there were more penpals. It was common to have pen-pals in foreign countries, or other places in your own country. Usually a pen-pal was someone you did not know, but you would write back and forth just like they were a friend. The internet has taken that away now, but as you can tell, many people send emails to friends they have never met, but we don't use pen and ink.