Short Definition
F1 score is the harmonic mean of precision and recall.
Intuition
F1 gives one number that punishes systems that do well on precision but badly on recall, or the reverse.
Technical Definition
F1 equals 2 times precision times recall divided by precision plus recall.
Example
A classifier with precision 0.8 and recall 0.6 has an F1 score around 0.69.
Common Misunderstandings
F1 ignores true negatives.
F1 is not always the right business or safety metric.