A single number that balances precision and recall, used when you need one figure to compare models by. It is the harmonic mean of the two, which means it punishes a model that is excellent at one and poor at the other. Convenient, but it hides the trade-off it is averaging, so it should never be the only thing you look at.
Technical view
F1 is twice precision times recall over their sum. The general F-beta form weights recall beta times as heavily as precision, so F2 suits screening where misses are costly and F0.5 suits situations where false alarms are expensive. For multi-class problems, macro-averaging treats every class equally and exposes poor performance on rare classes, while micro-averaging weights by frequency and is dominated by common ones. Stating which was used is essential and frequently omitted.
Related
Part of AI Terminology Index, section: Measuring Performance.