Reverse DNS is used to show relationship between an IP address and a domain name. To explain this, let's look at the following examples:

example.com (domain) → 1.2.3.4 (IP)

1.2.3.4 (IP) → example.com (domain)

Forward DNS record for domain "example.com" pointing to IP address "1.2.3.4" does not necessarily mean that the Reverse DNS for IP "1.2.3.4" also points to domain "example.com".

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".
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For example, the reverse DNS entry for IP "1.2.3.4" would be a PTR-record for "4.3.2.1.in-addr.arpa".

Reverse DNS is also different from forward DNS in which mechanism 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.
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However with Reverse DNS, your Internet Service Provider (ISP) must point (or "sub-delegate") the zone ("....in-addr.arpa") to your DNS server.
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Without this sub-delegation from your ISP, your reverse zone will not work.

Reverse DNS is mostly used for such things as tracking where a website visitor came from, or where an e-mail message originated. In that context, it is used by many mail providers as an anti-spam method which in turn can help with email deliverability and placement. 

See also: FCrDNS