ip6.int is the currently used DNS zone where
IPv6 reverse DNS information is kept.
Much like in in-addr.arpa, the reverse DNS zone for IPv4 addresses,
the addresses here are written "backwards", because of the need
for the structure of DNS information correspond with the ownership
of the actual address delegations.
The addresses in in-addr.arpa are written in decimal notation,
divided into octets. Because the usual IPv6 address representation
is in hexadecimal notation, the addresses in ip6.int are written
in hex, and divided into separate nibbles (four bits).
Thus for IPv6 address 1234:5678:90::1234:5678:90ab:cdef, the queried
reverse resolve PTR record is
f.e.d.c.b.a.0.9.8.7.6.5.4.3.2.1.0.0.0.0.0.9.0.0.8.7.6.5.4.3.2.1.ip6.int.
Yes, even I think they are ugly.
The ip6.int zone is described in RFC 1886 (DNS Extensions to support IP version 6).
According to RFC 2874 (DNS Extensions to Support IPv6 Address Aggregation and Renumbering), it's supposed to be replaced by the ip6.arpa zone, wherein
the address space delegations are to be made using few new DNS features,
notably DNAME records and "bit-string labels" (BITLBLs).
There has been some discussion about the ip6.arpa zone on IPv6-related mailing lists,
but so far the current situation is that all resolvers use the ip6.int zone.