The phrase is older than computer networking.

"Pen" means "caneta," for writing in ink on paper.

"Pal" means a friend.

It means "friends who communicate mostly by writing," "friendship by correspondence."

If someone on italki talks about being "pen pals," it probably means they don't want to use voice or videocalls, but would like to exchange letters with you via email.

A "pen pal" originally meant a person in a foreign country that you never met in person. You never visited their country, they never visited yours. You wrote friendly letters to them--with a pen, on paper. You mailed them. They would write friendly letters back. 

Organizations existed to help you find "pen pals" to write to.

Nowadays, people still do this by postal mail, but it can also mean someone you exchange email with. 

 it's part of a stock phrase, the word "pal" in "pen pal" doesn't have any special meaning. it doesn't imply romance, or anything like that.