When i do box jumps, or skateboard jump & lift my legs way up to my chest, i get this terrible pain in my lower right back, like a pulling. what is it?

Hard to be specific: Pain is the bodies signal that something is amiss. Focal pain suggests a muscle tear or nerve irritation localized to that area. A physical exam by your doc aided by a CT scan or MRI may show the trigger for this pain. Without these studies it is unlikely you would find out. You could just take it easy for a week or 2 & see if it self heals.

Strain: I believe that it's from straining the muscles and ligaments of the lower spine. The intervertebral discs are also being stressed with this maneuver. As a general rule it is advisable to avoid any actions that produce significant discomfort as it's often nature's warning to protect your body.