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This ability doubles the threat range of a weapon. Only piercing or slashing melee weapons can be keen. If you roll this special ability randomly for an inappropriate weapon, reroll. This benefit doesn’t stack with any other effects that expand the threat range of a weapon (such as the keen edge spell or the Improved Critical feat).
Source: https://www.d20pfsrd.com/magic-items/magic-weapons/magic-weapon-special-abilities/keen/
A critical threat is the chance to land a critical hit, to do so you 'confirm' the threat with another attack roll that hits.
example:
Longsword = 19-20 (2/20 on d20 roll) threat range, damage x2 if threat is confirmed
Keen longsword = 17-20 (4/20 on d20 roll) threat range, damage x2 if threat confirmed
Right click on the weapon. It shows the description there. Normally affixes seem to be purple context words that you can just hover the mouse over to get the description, but not all. Some like Holy/Unholy/Keen you actually have to click the weapon itself.
It doubles it. 20 becomes 19-20 (1 to 2); 19-20 becomes 17-20 (2 to 4); 18-20 becomes 15-20 (3 to 6).