Arbitrary Release Time Lag is a new feature that Canon introduced to minimize camera shake due to mirror movement in a DSLR.

In the past, savvy users have used the 2-second self-timer with mirror lockup enabled or similar techniques to achieve sharp results. The new feature gives a bit more flexibility with varying delays(1/8, 1/4, 1/2, 1, or 2 second). In practice the camera will raise the mirror, pause for the set delay, then the shutter will open for the appropriate amount of time.

The Artibrary Release Time Lag feature was introduced with a host of new enhancements to help with camera shake and ultimately produce motionless sharp images. This is especially critical with the high megapixel count of the two new cameras introduced, but of course any discerning photographer could benefit here.

Finally, one particularly interesting benefit of this new feature was pointed out by the preview on the-digital-picture.com:

The new feature is especially useful when the self-timer feature is not usable including during intervalometer/time lapse capture.

From the Canon EOS 5DS/5DS R press release:

To help maximize stability and minimize vibrations, Canon added a new Arbitrary Release Time Lag Setting in Mirror Lock mode in both models. In addition to the standard setting (press the shutter button once to lock the mirror, then again to release the shutter), the EOS 5DS and EOS 5DS R cameras offer new setting intervals of 1/8, 1/4, 1/2, one and two seconds, releasing the shutter after the selected preset delay, allowing potential camera vibration to dissipate before shutter release.