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A "nail biter" is an expression that describes an event that is very exciting and/or tense. This can be tense in a good way, or tense in a bad way; in short, any situation in which the anxiety is such that it makes you want to bite your finger nails.
Friend One:Did you watch that horse race the other day? Friend Two:Yea. It was really close, a real nail-biter.
I just went to see the new horror film at the cineplex. Talk about a nail-biter. I had my eyes closed almost the entire time.