When you stay calm under pressure, you keep your composure. Keeping your composure for a skinned knee? Easy. Keeping your composure during an avalanche? Not so easy.
The word composure is from the related word composed, but don't think of the word in the musical sense. In this case, composed means calm. What's the difference between the two? Well, composed is an adjective, so you simply are composed. Composure, on the other hand, is a noun, so you can lose, keep, regain, or maintain your composure — your ability to stay calm. If you lose your composure, you're freaking out.