Used (1) for discrete classification (if an instance's predicted probability exceeds a threshold, classify as TRUE, otherwise FALSE), or (2) for discretizing/binning continuous data. *If you are tempted to use this tag, PLEASE read the tag wiki!*
Either usage of thresholds is usually an error for our purposes.
Using thresholds for discrete classification
The statistical part of modeling should extend to outputting predicted class membership probabilities. Deciding whether to treat a particular case as a member of a certain class is based on this probability, but must also consider the costs of misclassification. More information at Classification probability threshold.
Predicted probabilities and thresholds are often used to calculate accuracy. Related to the point above, accuracy is not a good measure for assessing classification models.
Using thresholds to discretize/bin continuous data
Discretizing or binning continuous data typically throws away a lot of information and introduces step changes that are rarely found in actual data generating processes. It is usually better to model nonlinearities using splines. For more information (despite the title), see What is the benefit of breaking up a continuous predictor variable? (Answer: none.)