Compensation Delay Line is a metric based delay to compensate differing positions of microphones or speakers.
For example, you have recorded guitar with two microphones placed in different location. Because the front of sound wave has fixed speed in normal conditions, the phasing of microphones can vary and depends on their location and interposition. The best sound mix you will get when these microphones are in phase (synchronized). Note that distance of ~30 cm between microphones makes one microphone to capture signal in antiphase to another microphone. That makes the final mix sounding moody. This plugin helps to solve phasing problems by adding different delays to each microphone track and make them synchronized.
Another possible application it the compensation of PA speakers in a live concert setup. If speakers are placed inside the audience compensate them against the FOH speakers left and right to the stage to avoid echoes or phasings within the audience area.
How to synchronize microphones:
The best result can be reached when you take one track as base and synchronize other tracks one by one with it.
Remember that synchronization/delay tolerance depends on sample rate, too. Higher sample rates will give more tolerance.