Nail-biting describes something so tense and exciting that you cannot relax while you watch or wait, because you truly do not know how it will end. The picture behind the word is a person chewing their fingernails while they wait — nervous, but not able to look away. We use it for football and basketball games that stay close until the last second, for elections where nobody knows the winner until late at night, for films where the hero might not escape, and for waiting for exam results or a hospital phone call. It is almost always used before a noun: a nail-biting finish, a nail-biting match, a nail-biting hour. It carries a mix of fear and pleasure. For a game or a film, the fear is enjoyable — people say it as praise, meaning "that was wonderful, my heart was racing". For real bad news you are waiting on, the fear is real and the word only means the waiting was hard. So a nail-biting film is a compliment; a nail-biting week in hospital is not. The word is common in newspapers, sports reporting and everyday speech, and it is neither formal nor rude — you can use it with anyone. Note that biting your nails is also a real habit some people have when nervous, and that plain verb use (he bites his nails) is separate from this adjective.