A pen pal is a person far away with whom you communicate by letters. In the last century, we did this by sending letters in the mail and waiting for an answer. Nowadays people do it by emailing each other. 

Normally, the idea of a penpal is NOT simply to have a friend, and so it should not be a far-away cousin, for example. It could be a friend who moved away, but even that is not the most common example. Normally a penpal is someone you didn’t know before, and you write to them to learn about life in a place different from where you are. It doesn’t have to be another country, but it should give you the opportunity to learn something new, in a way that is more fun that reading about it in a textbook. 

Penpals have always been very popular for people learning languages. I had a penpal when I was in high school. My French teacher exchanged names with a teacher in France and everyone in my class got the name and address of a French teenager. I wrote letters to my friend who lived in Paris, and she wrote letters to me in the U.S. Many years later, I was able to meet her and her parents in France, but all of our friendship, other than that very brief meeting, was by letter. It was a fun experience and I learned a lot.

A penpal relationship is often used to practice writing and reading in a foreign language, improving literacy, to learn more about other countries and life-styles, and to alleviate loneliness.