It’s the “Big W” !
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Quaternions have W. Very few people understand them.
Good luck.
Yes Quaternions are hard to understand and work with, at least to most common mortals…
They don’t suffer gimbal lock, for that it’s good, but you’ll notice that values are inter-dependant.
If you switch the bone to euler mode and want to make the bone spin on one axis, you just have to set two keyframes for that value. Rotation are also expressed in Degrees so it’s easy to understand.
With quaternions it’s impossible to make a bone spin on itself by just setting values.
X,Y,Z values aren’t expressed in degree or radians either.
From what I understand, Quaternions are similar to vectors, X,Y,Z values are locations and accumulated they form an orientation. What about the W ? Frankly I don’t really know.
In various shows I worked on animators tend to prefer very much working with Euler , even if they have their issue.
Quaternions, Axis Angle, Euler, 3 different ways to express rotation, all with their issues.
That said, if you don’t plan to edit F-Curves and work only with keyframes without entering manual values in the transform panel, you should be able to manage with quaternions.
So…if I am doing using add-ons like this:
https://rbfdrivers.readthedocs.io/en/latest/user-guide/inputs/
Which I purchased thanks to @joseph [does not work for Blender 3.1.2 by the way] can I just check W instead of doing X, Y and Z, is this W magically representing all three X, Y , Z or the W also require X and Y and Z ? Is the W somekind of “memory” as to how many time the object turned on their X or Y or Z ? Sorry.
No that’s more complicated than this. Even if I don’t really understand how they work.
Better to switch to Euler, at least rotation will makes more sense.
This video explain the gimbal lock problem, and will help you to choose the best order of rotation :
I though they’ve done one about quaternion too but I didn’t find it…
You can, generally speaking, ignore the W and just rotate things visually until they look good. With that specific add-on, you’ll have your best luck by sculpting shape keys that the RBF drivers control. This is the recommended workflow by the add-on creator
Just change Any quaternion to “XYZ Euler” and it will all make sense again.
Good luck!
Thank you @joseph I will ignore the W.
Thank you @sozap for the cool video.
Thank you @calpgrmr, but I asking in relationship to the add-on mentioned that DOESN’T WORK for Blender 3.1.2, but thank you for your intention to help 
And thank you for that lovely W tree pic
If you have time and want to try to understand Quaternions I found these 2 videos very good (although I have forgotten most of it now 
)
Be warned you will probably have to watch then a few times to keep up!
The film was epic !! by the way.