Why is the ratio between action potential and threshold value called the 'safety factor'?
Action potentials propagate by depolarization of one section of the membrane causing depolarization of an adjacent section.

It is necessary that this depolarization be greater than threshold. If the amplitude of the action potential were to drop below threshold, it would fail to propagate. Additionally, it would be quite slow and inefficient.

Therefore, the action potential amplitude is far greater than the threshold. This helps speed and builds in a "safety factor" to ensure the action potential propagates - that's what your book is saying.