Quaternions, or quaternion rotations, are a special way to allow rotations to avoid the dreaded “gimball lock” condition. Quaternion rotations enforce a “shortest distance” rule. For any rotation less than 180 degrees from the starting rotation value will complete successfully. However, if you attempt to rotate at a greater angle, then you will see that the object will “snap back” as it’s rotating. Hence, “shortest distance.” All that means is that you must either animate accordingly, or opt for the original Euler-based rotation system.
The best way to see if Quaternion rotations are going to work for you in your scene is to try them out. Get a feel for Quaternions, and you will soon see when to best leverage them to your benefit. Many characters can use Quaternions effectively, since most hinge joints, like knees and elbows, do not pass 180 arcs. However, ball joints like the shoulders and hips just might. Again, test for yourself and decide if the results will work for you.