Official comment
Link Mode is for using the computer as the music source; the CDJs do the grunt-work, rekordbox serves up the files. This basically has the CDJs operating the same way as if they had a USB drive connected to them. You would use an ethernet hub to connect your players and computer.
Performance mode (HID) allows you to use the CDJs as controllers for the rekordbox dj software. This requires the purchase of a rekordbox license (if you don't already have one from a hardware purchase), and uses USB cables to connect the players (and/or mixer) to the computer.
Which you should use is up to you - there are some benefits of using the software in link mode (eg. if you have a lower-spec computer and don't want to burden the computer with the mixing work), or performance mode (additional features and functions not available directly on the players).
