probably a silly question, but since i haven't seen superman cards or new genesis cards played at all I'm not sure what cosmic means.

A character with cosmic comes into play with a cosmic counter. Usually they say what the cosmic counter does after it states cosmic in bold. When a character is stunned thy lose their cosmic counter and thus the ablity written after cosmic. A counter only comes back if you either re-recurirt the character or use an effect like mother box or star labs to get another counter.