I just need to better understand how the IK works. So, what does the “Stretch” option do?
I know what “Rotation” does. It lets the chain of bones follow the rotation of the target bone. But I still can’t figure out what the “Weight position” does!
What are the values next to the Rotation & Position? I thought they are like the “Influence” but they don’t really affect the animation of the chain of bones when I animate the target bone.
Thank youuuu 
It is a bit hard to explain so I have made an example file, if you select and move the target bones you will see what I mean: IK.blend (156.1 KB)
Stretch allows you to choose a bone in the IK chain and make it stretch to position, you have to select the bone you want to stretch and in its bone properties tab under “Inverse Kinetics” enable the stretch option (with the slider). Select the stretch target and move it about to see what it does.
The weight position sliders take effect when there is a “tree-IK”.
This is when 2 (or more) different Ik chains both influence the same bones (like branches of a tree),
In the example file select the tree IK’s targets and move them about.
You will see that the one that has full weight will pull the other side away from its target, were as the other one with 0.01 weight will not pull its counterpart away from its target.
Hope this helps.
Edit: the stretch function is especially useful for mechanical rigging:
Wow you did a great job… Thank you sooooo MUCH for this great effort to help me. I really appreciate it. You’re wonderful 