PCI DSS stands for 'Payment Card Industry Data Security Standard'. This is a set of security requirements created by the Payment Card Industry, laying out what Merchants need to do to protect customer information. The PCI Council (which is an industry body made up of organizations like Visa, MasterCard, American Express, Discover, etc.) requires that Merchants meet this set of security requirements if their business accepts, transmits, or processes customer payment cards (such as credit cards or debit cards). 

Merchants that do not comply with these requirements can be penalized in a number of ways, up and including having their card-processing privileges revoked, leaving them unable to accept customer payment cards.

Get a copy of the PCI DSS.  It should be noted that this site gives Merchants additional tools and advice to help them deal with the requirements of the PCI DSS.