This is really kind of an old-fashioned word. Back in the 1920’s and ’30’s it was used by kids to give a stamp of approval to whatever they like a lot. It was considered a slang word back then, and was keenly disapproved of by the parental generation. Lots of things were changing in American culture, as well as in the rest of the world. Some of the changes were keen, others not so much 🙂
One usage of the word stems back to the Irish caoinim, meaning I wail. One would keen over the loss of a loved one; a fussing baby or teething toddler keened over his misery.
Mostly, though, when I think of keen I think of someone of a very sharp intelligence, and also a sharp wit. I love to be around people who have a keen sense of humor. Laughter is the best medicine, after all.
As with so many other English words, there are multiple meanings and uses of keen. No wonder English is difficult to learn. Difficult, but certainly not impossible.