Seriousness is a quality of being calmly intent, or serious. Your seriousness will serve you well when you're studying for an important test.
You might talk about the seriousness of an argument between two friends, or the seriousness of your math teacher when she expects the class to pay attention. Sometimes seriousness implies a bit of worry, like when you ask about the seriousness of your grandmother's health problems. The noun seriousness comes from an adjective, serious, with a Latin root, serius, which means "weighty, important, or grave."