Basically when you use Subdivision Surface Modifier things get rounded up and smooth, so you need to hold things in place. You add the holding edges to stop the geometry from smoothing or drooping. It's kinda hard to explain. Think about it like Hollywood stars plastic surgeons, they start to get old, skin doesn't hold up like it used to, they hate it and they go to a guy that keeps things in place, that's what holding edges are doing basically, they are the cosmetic surgery of polygons.
Check out this lesson: to see JL doing some examples:
https://cgcookie.com/lessons/subdivision-surfaces
Or the modeling bootcamp for a full dive:
