PCI refers to the Payment Card Industry.
PCI compliance, in this context, refers to complying with the PCI Data Security Standard.
Essentially, the PCI Data Security Standard is a worldwide security standard for information which was assembled by the PCI Security Standards Council. This standard requires a minimum level of security on servers and is designed to assist companies and organisation that deal with debit and/or credit card payments, in an attempt to reduce fraud.
PCI compliance applies to all entities which deal with information of card holders, either via the processing, holding or passing on of cardholder information. The PCI Data Security Standard (or DSS) requires the following of the network(s) and/or server(s) on which the cardholder information is sent through or stored.
PCI compliance also reference wireless networks and their use, monitoring and security incident responses. Due to the inherent issues of transferring data wirelessly, PCI compliance requires at least quarterly security checks of any wireless networks in use and sets a minimum security standard for said wireless networks.