How can I communicate between two computers on different networks via server?

So I've been thinking of making a small side project just to learn about computer communication and I thought that a simple messaging desktop app or web app would be the perfect project.

I've learned that you can communicate between two computers on the same network by using their IP address and an open port to transmit data. The thing is, what I would like is sorta like a server/database that stores the messages and some way to identify a user (Email, username, etc...) so that I can send him a simple text message without having to manually type his IP address or having to be on the same network.

I'm new to this kind of stuff so maybe my wording is not right or I'm asking the wrong questions, sorry if that's the case.