What is Negative Space?

I got interested in Negative Space when I encountered the artwork of Coles Phillips.  He was an early 20th century American artist and illustrator who created many magazine covers using negative space.  By using one color for both the background and large parts of the rest of the composition he could keep down the number of ink colors which greatly saved on printing costs (and made him popular with magazine editors).  His compositions are intricate and appealing.  But what IS negative space?

I admit I am confused by the modern quilting movement.  The definition of it seems a bit nebulous, but negative space is regularly mentioned as an integral part of it.  But when I look at a lot of modern quilt designs, they don’t have negative space in them.  So I’m researching it and collecting negative space images, hoping that it will eventually penetrate into my brain.