Any important situation is serious, and this word is also the opposite of humorous and playful.
If you're frowning, someone might say, "Why so serious?" This is a word for people and situations where there's no fooling around. If you're staring at the computer screen, typing quickly, you look serious. If you are in a car accident, that's a serious situation. Some people are more serious than others. If you're always making jokes and smiling, then you're not that serious. One place everyone needs to be serious is at a funeral home.