An AAAA (pronounced quad A) record is a DNS record that maps to an IPv6 address.

For example:

~: dig ns1.no-ip.com AAAA

;; ANSWER SECTION:
ns1.no-ip.com. 86400 IN AAAA 2620:0:2e60::33

AAAA records are available for all customers.

Currently, IP addresses are based on version 4 of the internet protocol, where there are 4 sets of numbers ranging from 0-255. For example (127.198.30.245).

What is IPv6?
IPv6 has a much larger address space where there are 8 sets ranging from 0000-FFFF.
For example (2001:0db8:0000:0000:0000:0000:1428:57ab).
IPv6 also has protocol enhancements for security as well as many other features.

IPv6 is not readily available from most internet service providers and is not widely used to date.  IPV6 adoption is increasing as we run out of IPV4 address space and will become more relevant in the coming years.

For more information on IPv6 please take a look at the IPV6 wikipedia page.