Jekyll is explaining the opposites (good and bad) within a person are always fighting to get the upper hand. And that niether can truly win.
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Jekyll is describing the eternal battle between good and evil within his own mind. The "polar twins" refer to the opposing forces of his dual nature, with good represented by Dr. Jekyll and evil by Mr. Hyde. This internal struggle is ongoing and agonizing for Jekyll as he tries to control and reconcile these conflicting sides of himself.