The quote refers to the attempt at going beyond the limitations of human perception. For instance, the human brain is finite, and thus cannot quite grasp infinity. If we were to break away from our human frailty, somehow escape our human limits (our human nature), we could then understand infinity. Lovecraft warns that to do this, to suddenly perceive and understand what humans can t, is to either go insane (having "broken" our minds) or cease to be human. This often happens in Lovecraft s stories: a human sees something or does something that causes them to perceive a "truth" that cannot be processed by their finite brains, and thus they go insane or become part of the phenomena (usually a monster of cosmic horror).