Reverse DNS
Reverse DNS is exactly what it sounds like - the reverse of normal DNS. Normal DNS maps your domain name to your IP. Reverse DNS maps your IP to your domain name.
Reverse DNS is required by some Internet protocols and by extensions to some other Internet protocols. Without reverse DNS, you will experience trouble with r-commands, IRC, some SMTP servers, most enterprise management systems, and many network backup systems.
Troubleshooting problems caused by faulty or non-existant reverse DNS can take considerable time and effort. It is much better to ensure that reverse DNS is configured correctly from the beginning.
Reverse DNS is setup very similar to how normal (forward) DNS is setup. The owner of the IPs needs to delegate the reverse DNS to your authoritative name servers. The owner of the IPs is usually the ISP or the hosting provider.
For reverse DNS you will have to setup your reverse DNS domain. This is a special domain that ends with "in-addr.arpa". This domain is created in your DNS service in the same manner as any other domain. You will need to ask the organization that owns those IPs (usually your ISP or your hosting provider) what domain to make.
Then you will have to have the organization that owns those IPs (usually your ISP or hosting provider) delegate the reverse DNS for your IPs to your authoritative name servers (similar to how you delegated the DNS for your domains to your authoritative name servers).
If you only have a few hosts that you need reverse DNS for, it may be easier to just have the owner of those IPs set the entries in their reverse DNS domain for your hosts.