"Reverse DNS" is the term given to the ability to look up a name from an IP address, as opposed to the usual use of DNS to look up IP addresses and other resources for names.
Reverse DNS actually uses the same query methods as normal DNS, but uses a special zone called in-addr.arpa. Under in-addr.arpa the zones have numeric names corresponding to the numeric values of octets of IP addresses. These zones are then delegated to the owners of the corresponding address space.
Since domain names are significant from right-to-left, while IP addreses are significant from left-to-right, in order to properly represent suballocation of IP address space it's necessary to specify the numeric values of the IP address from right-to-left under in-addr.arpa. Also, reverse DNS uses a specific PTR resource record type. So a query to obtain the name for IP address 128.223.142.97 would be done as:
$ dig 97.142.223.128.in-addr.arpa ptr ;; QUESTION SECTION: ;97.142.223.128.in-addr.arpa. IN PTR ;; ANSWER SECTION: 97.142.223.128.in-addr.arpa. 86400 IN PTR hexadecimal.uoregon.edu.
(much of the less relevant dig output has been elided).
Note that delegation for in-addr.arpa subdomains is done separately from domain names. While a domain holder gets that domain name delegated to it (or him or her) as a zone of authority, it's not always the case that the same is done for the IP address space hosting the systems in that domain. ISPs may choose to manage (or at least refuse to delegate) the reverse DNS for the IP address space delegated to them.