It's cute shorthand for the two functors \$$a \wedge \cdot\$$ and \$$a \to \cdot\$$.

I wrote a little puzzle a while ago to implement this particular adjunction in Haskell: https://forum.azimuthproject.org/discussion/comment/16072/#Comment_16072

People use the monad associated with their closure operator is used all over the place in parsers and interpreters.