DNS can mean either domain name server or domain name system. Either translation of DNS stands for a database of Internet names and addresses that allow information to be routed from one place to another. The destination of any Internet request is an IP address, but most people have a hard time remembering an address like 192.168.234.7. So they use an address like www.ibm.com, and then the DNS translates it into the IP address.
Reverse DNS turns an IP address into a hostname -- for example, it might turn 192.0.2.25 into host.example.com