but I still don't really understand what a port actually is and how it works.
I don't think it's up to the blitz manual to point out the basics of networking. After all, the manual doens't explain how to do other basic things like clicking your mouse either.
Anyway, a port is just a number that is used by the computer to identify which program it has to send the data to.
For instance, if you have a webserver program running and you've got it configured to listen to port 80 (default for web), and browser makes a connection to your computer on port 80, your computer will send it to the webserver program.