How does a cover crop create nutrients out of thin air?

Image by chesbayprogram
Cover crops on a farm field with a red barn in the background at Merkle Wildlife Sanctuary

Question by FORMER Atheist Now Praising FSM!: How does a cover crop create nutrients out of thin air?
I’m having difficulty understanding how a cover crop adds nutrients to a soil when any plant growing in any given soil is ostensibly taking nutrients OUT in order to grow.

Against the background of the law of conservation of matter, how does a cover crop do anything more than merely cycle what is already present?

http://en.wikipedia.org/wiki/Conservation_of_matter

Add your own answer in the comments!