People with a better PID get better response times and stuff, for example: if you have a bad pid and you follow someone with a good pid theres a big chance you get stuck behind a fence. (Remember when those guys took the flag at castlewars and just rambo'd out without anyone getting a single hit on then?)
The person with the best PID will also get the first hit in a duel.
Jagex has used different PID systems over the years, the current PID calc system for osrs is based on the last octet of your IP address.
The lower the better, so if you have an IP address ending in 1 (x.x.x.1) its very likely that you get a good PID and thus get first hit in duels.
"VPN" in this context just means proxy, a server between you and runescape that masks your IP.
If your computer's IP ends in .232 but you have a proxy (or VPN) that ends in .1, you could use that proxy to play on runescape to get better pids.