In statistics, there are Type I and Type II errors.
A Type I error is when we reject the null hypothesis when it is true. (False positive)
A Type II error is when we accept the null hypothesis when it is false (False negative)
Statisticians spend most of their time trying to minimize one or both of these types of errors. They might look at precision (true positives / true positives + false positives) and recall (true positives / (true positives + false negatives).
Different problems have different costs associated with Type 1 and Type 2 errors. For example, false positives (type 1) may be more acceptable than false negatives (type 2) in medical diagnoses. The cost of missing a diagnosis can be high.
Or look at biometric matching – like facial recognition or fingerprinting. If it is used for authentication, then false positives can be costly (authenticating the wrong person).
Finally spam email classifiers could aggressively filter spam and reduce the amount of emails that arrive. But, the cost of identifying a legitimate email as spam could be very costly, so spam classifiers often accept more false negatives (spam not detected as spam) than false positives (spam detected as spam).