Other forms: mustered; mustering; musters
Originally meaning "to gather soldiers," muster has been expanded to include gathering up just about anything — you can muster up some dinner, some friends, or even some ketchup, pickles, and mustard.
Remember that muster used to involve getting reluctant soldiers out of bed and into the field of battle — so it involves overcoming a certain inertia. When you muster up the courage to face something, it's clear that this is pretty scary for you.