"Surprising myself, I press on the blade and slowly draw the knife across my forearm. Nothing happens. Huh. Repeating the act, I press harder with my palm on the tool's grip. Still nothing. No cut, no, blood, nothing. Extracting the short knife, I vigorously saw back and forth at my forearm, growing more frustrated with each unproductive attempt. Exasperated, I give up." (page 165, said by Aron Ralston.)
This quote is important because it explains how tough it was for Aron to amputate his arm. This is his first attempt, which was on the third day. However, Aron actually cuts off his arm on the fifth day (so the quote is about his first attempt). Being that this whole book is based upon Aron's self-amputation, I feel this quote can fit the category of "important".