What's the difference between Ctrl-Alt-F1 and Ctrl-Alt-F3?

Besides the number there is no difference.

There are some examples where more than 1 tty is useful.

1. tail -f {logfile} will show new entries that are added in the logfile. Where you can use another tty to start, stop a service or do some kind of command line instructions, or do something in mysql.

2. same goes for analyzing CPU usages on your system: have sar or top/htop run on 1 tty and then use another session to start a browser, a command or service and by switching tty you can check what happens.

And yes you can do that from a terminal in the desktop but not everyone has a desktop ;)