Utterly means completely, totally, and absolutely, with nothing left out. When something is utterly destroyed, there's nothing remaining. When you're utterly confused, you don't understand even a tiny bit. When someone is utterly exhausted after running a marathon, they have zero energy left.

The word adds force to whatever comes after it. Compare “I disagree” to “I utterly disagree.” The second version makes your position much stronger and more definite. If you say a movie was boring, that's one thing; if you say it was utterly boring, you're emphasizing that it was boring from start to finish, without a single interesting moment.

You'll often see utterly paired with extreme words: utterly silent, utterly ridiculous, utterly brilliant, utterly impossible. It emphasizes that there are no exceptions or qualifications. When a teacher says the classroom became utterly silent before announcing test results, she means you could have heard a pin drop: not a whisper, not a shuffle, nothing. The word works like a volume knob turned all the way up, making whatever you're describing as intense as it can possibly be.