IPv6 is Internet Protocol version 6. It is the successor to version 4 (IPv4). Currently the Internet consists of a mix of IPv4 and IPv6. For more information in general, see the Wikipedia article on IPv6.
UnrealIRCd makes use of the "dual IP stack" of your system, meaning it can listen on both IPv4 and IPv6 addresses. UnrealIRCd is always built with IPv6 support. To actually use IPv6 you'll need an IPv6 address on your machine and an ISP that does IPv6 routing (unless you want to tunnel, but this is outside of the scope of this article).