An IPv4 address looks like 203.0.113.7. There are about four billion of them and they ran out years ago, so each one has a price. An IPv6 address looks like 2001:db8::1, and there are so many that networks hand them out in huge blocks.
The catch is on the website's side. A site must be reachable over IPv6 for an IPv6 proxy to open it. Most large platforms are; many small sites are not. You do not need IPv6 on your own connection: you reach the proxy as usual and only the exit uses IPv6.
Read next: IPv6 proxies explained