When you do something calmly, you're cool and peaceful about it. Screaming hysterically for your mischievous dog to come back won't work, but if you calmly call his name, he'll probably come running.
Doing things calmly means they happen easily, without any disturbance or strong emotion. That can include breathing calmly to reduce stress, speaking calmly to someone who's upset, or watching the gentle breeze blow calmly across the surface of a lake. The adverb calmly comes from the Old Italian calma, which means both "quiet" and "fair weather," and its Late Latin root cauma, "heat of the midday sun."