Keen doubles the range which you need to score a critical hit.
For instance, if you have a weapon that needs to roll 19 or 20 to score a critical hit. Then the keen attribute will make it so you only need to roll 17 to 20 instead.
This is very useful when a character has an ability that increases their chance of scoring a crit. Put the two together--the crit ability, and "keen," and you have a much greater likelihood of really wallloping the daylights out of an opponent early in a battle.
To the Righteous belong the fruits of violent victory. The rest of us will have to settle for warm friends, warm lovers, and a wink from a quietly supportive universe.