Pairing records are used to identify which PCs are "trusted" by a device. They are created by iTunes whenever a device is connected to a PC and unlocked (iOS 7+ also requires tapping "Trust" on the device). Pairing records are saved as PLIST files, and are named using each device's unique identifier (UDID, see How Can I Determine The Unique Identifier (UDID) Of A Locked Device?).
They can be found in the following locations:
OS X: /var/db/lockdown