Tasting Inner Peace

I've always heard that the utmost point of inner peace, and maturity as been achieved when a person can remain calm even in the face of adversity.

I wasn't exactly sure what that meant. I mean, I know what the words mean. I know what the sentence means. But, what I was unsure of, what I halfway admitted to myself was that I was not clear on what that would look like unfolding in real time. How would that feel, and how would I know when I have reached that level?