The Payment Card Industry Data Security Standard is a standard your business must meet if it processes credit card details. This includes online credit card transactions processed through an eCommerce website. The standard was put in place by the credit card companies to reduce credit card fraud.
The PCI DSS has 12 requirements within 6 categories. In reality, the number of requirements are much higher than this, as each of the 12 requirements have several sub-requirements.
Complying with the PCI DSS can be a huge cost for businesses. Thankfully you can sidestep most of the requirements by using a Tier 1 PCI DSS compliant payment gateway. Most of the PCI DSS requirements are related to storing credit card data. By using these payment gateways, credit card numbers are never actually stored anywhere on your business systems and most PCI DSS requirements become irrelevant to your business. PCI DSS compliance becomes a self-assessment questionnaire.
One advantage to being deemed PCI DSS compliant, is that you can mention it on your website to increase trust with your customers. If you use a payment gateway you can request a certificate of compliance from them for this purpose.
You can read more about PCI DSS at this Australia Post Business Lounge article and the Wikipedia PCI DSS article.