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The dead simple explanation of precision and recall

Most beginner machine learning practictioners get confused with these two metrics that are the heart building any successful ML model.
Task: Classify cat/not-cat
After classifying bunch of images:
Precision:
Just take the ones that are predicted as cat.
How many of those images were actually cat?
Recall:
How many % of cats were correctly recognised by the model?
Which one is better?
It seems both of them needs to be better metrics for our model. But should precision be high or should recall be high? Or should both of the them be high?
That’s where F1-score comes to play:
F1-Score:
It is the average(actually a harmonic mean) of precision and recall. So whichever has better F1 score wins.
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