What exactly is arrow spine? Why is it important? Does it deal with the stiffness of the arrow? Will having the wrong arrow spine make your arrow look as if it is wobbling side to side, or shoot inconsistent groups?

I shoot ACC 3-39's, at 65lbs, with a 29in draw length and the arrow length is 29in. What can someone tell me about this set up, is it right or wrong?

I recently splintered a limb on my bow and I was wondering if this may have had anything to do with it, because I do not know if I am shooting the correct arrow spine for my set up or not.