Say "perempt-" out loud. Hear how it sounds like you're clearing your throat as if to get everyone's attention and put an end to a discussion? That's all you need to know to understand peremptory, which means bossy and official sounding.
Peremptory is used to describe commands, statements or orders of the kind that people obey because they are given with an air of authority — they are often barked. Think of doctors in operating rooms, growling peremptory commands at nurses, "Scalpel," "Forceps," "Chewing gum," and you'll get the idea.