Particle interactions in the atmosphere. Courtesy of Jim Madsen University of Wisconsin-River Falls.
So why study neutrons? Where do they come from? For the most part this has to do with the sun. When we study neutrons we can learn about the sun. But the neutrons don't come from the sun itself.
The sun can be very active. Changes in the sun's active surface can get it to eject high energy particles (from solar flares coronal mass ejections or related phenomena) . Some of these particles can get sent toward the Earth. As they hit the atmosphere they can collide with the nuclei of atoms in they atmosphere. These collisions can cause the nuclei to break up. The neutrons are part of what comes out of such collisions. So studying such collisions can help us learn about solar activity. That is a good thing to do because the particles that come of of the sun can cause problems. They can disrupt satellites, electronics, and the electrical infrastructure (see http://gizmodo.com/what-would-happen-if-a-massive-solar-storm-hit-the-eart-1724650105 for more information on that).
The sun ... It's all smiley and whatnot.
Solar flare! (Not to scale)
Particle coming from the sun ... (Even MORE not to scale)
Collisions cause secondary particles (like neutrons!) ... (Still not even close to scale.)