If you have a keen interest in something, you are really, really into it. Keen is an adjective that describes something that is intense, sharp, or focused.
The adjective keen comes from the Old English word cene that translates to "bold and brave" and while the spelling is now really different, the sounds are similar. Variations of keen as being "bold" and "strong" show up in other languages like Old Norse, German, Dutch, but apparently only English has the meaning of "sharp" — relating to "an edge or blade." Keen has a lot of close — and brutal — synonyms, such as caustic, cutting, piercing, and penetrating!