Reverse DNS
Reverse DNS is IP address to domain name mapping - the opposite of forward (normal) DNS which maps domain names to IP addresses.
A mail servers that send mail need to have a Reverse DNS in order to be sure a receiving mail exchange server accepts the incoming connection. This is something that is provided by your Internet Service Provider (ISP) and they do not normally allow this to be changed.
Overview of Reverse DNS
Reverse DNS is separate from forward DNS. Forward DNS for "abc.com" pointing to IP address "1.2.3.4", does not necessarily mean that reverse DNS for IP "1.2.3.4" also points to "abc.com". This comes from two separate sets of data.
A special PTR-record type is used to store reverse DNS entries. The name of the PTR-record is the IP address with the segments reversed + ".in-addr.arpa". For example the reverse DNS entry for IP 1.2.3.4 would be stored as a PTR-record for "4.3.2.1.in-addr.arpa".
Reverse DNS is also different from forward DNS in who points the zone (domain name) to your DNS server. With forward DNS, you point the zone to your DNS server by registering that domain name with a registrar. With reverse DNS, your Internet connection provider (ISP) must point (or "sub-delegate") the zone ("....in-addr.arpa") to your DNS server. Without this sub-delegation from your ISP, your reverse zone will not work.
Reverse DNS is mostly used by humans for such things as tracking where a web-site visitor came from, or where an e-mail message originated etc. It is typically not as critical in as forward DNS - visitors will still reach your web-site just fine without any reverse DNS for your web-server IP or the visitor's IP.
However reverse DNS is important for one particular application. Many e-mail servers on the Internet are configured to reject incoming e-mails from any IP address which does not have reverse DNS. So if you run your own e-mail server, reverse DNS must exist for the IP address that outgoing e-mail is sent from. Note: it does not matter what the reverse DNS record for your IP address points to as long as it is there. If you host multiple domains on one e-mail server, just setup reverse DNS to point to whichever domain name you consider primary. (e-mail servers checking for reverse DNS do recognize that it is normal to host many domains on a single IP address and it would be impossible to list all those domains in reverse DNS for the IP).
Getting reverse DNS for your IP addresses delegated to your own DNS server
Reverse DNS is controlled by whoever "owns" the IP address. The owner can choose to sub-delegate reverse DNS for a range of IP range to someone else, who in turn can sub-delegate parts of that range further, etc.
IANA ultimately "owns" all Internet IP addresses. IANA delegates these IP addresses to 5 regional registires; AfriNIC (Africa), APNIC (Asia/Pacific), ARIN (North America), LACNIC (Latin America), and RIPE (Europe, Middle East, Central Asia). And these registries delegate their IP addresses to backbones providers and ISPs, who delegate to end-users.
So as an end-user, if you want control of reverse DNS for your IP addresses, you need to contact whoever provides you with these IP addresses, and ask them to do a reverse DNS sub-delegation to your DNS servers.
For example if your IP range is 1.2.3.0 to 1.2.3.255, then the reverse DNS sub-delegation is typically done using a DNS zone name "3.2.1.in-addr.arpa". If you have less than a class C (256 IP addresses), then the reverse DNS sub-delegation uses a slightly different format called "Classless IN-ADDR.ARPA delegation". The exact zone name format used for this vary for each ISP, so it is very important that you setup your reverse zone on your DNS server with the zone name provided by the ISP.
If you only have one or a few IP addresses, most ISPs will not do reverse DNS sub-delegation for this at all. However in most cases, they will point reverse DNS for your IP addresses to whatever domain name that you want, at least if you are a business customer.