What is binary classification?
Binary classification is classification with exactly two possible outcomes. The model outputs a score, typically a probability that the record belongs to the positive class, and a threshold converts the score into a yes or a no. Whether a loan will default, whether an email is phishing, whether a part will fail inspection, and whether a patient will be readmitted within thirty days are all binary problems. Logistic regression, gradient-boosted trees, and neural networks all serve as binary classifiers.
Because there are two answers, there are two ways to be wrong. A false positive flags something that was fine. A false negative misses something that was not. The confusion matrix lays out all four outcomes, and precision, recall, specificity, and the ROC curve summarize them.
Why binary classification matters
The two errors almost never cost the same. A distributor predicting which invoices will be paid late loses a little goodwill for each false positive, when credit control calls a customer who was about to pay, and loses real money for each false negative that slips into bad debt. Moving the threshold trades one error for the other, so the decision belongs to the business owner of the process rather than to the data team. Ask any vendor of a binary model for its precision and recall at the threshold it proposes, and for how both change when the threshold moves.