Ridge Line - Two types of ridgelines.
First, the structural ridgeline is very tight, non-stretchy, and sets the amount of sag on the hammock. When you pull the hammock supports tight, you're also pulling the ridgeline tight...but since the ridgeline holds a fixed length, the fabric in the hammock body isn't affected. Tom Hennessy has a patent on this kind of ridgeline so other hammocks can't be sold with it, but you can make your own or add it on to another model with no issues. I like it b/c no matter how you hang your hammock, it always has the same amount of sag. Also, you can tie the supports to the tree at a lower level and still have a comfortable hammock b/c it increases the sag.
Next, non-structural ridgelines are just strung up support bugnets or tarps and don't change how the hammock sags. Some of these are elastic and some are cord, occasionally webbing on some homemade ones.
Both kinds are good for holding boots, jackets, stuff sacks with nighttime essentials, etc. I always hang my headlamp and emergency whistle up there...that way I can blow the whistle when a bear comes sniffing and never have to leave the hammock. Since I switched to a soft-sided Nalgene I use my water as a pillow, but before that I always had a stuff sack with a snack and bottle of water hung on the ridgeline.
Hammock ridgelines are also different from tarp ridgelines. Tarp ridgelines are sometimes just a sewn seam running along the center length that needs to be sealed, and some folks actually run a cord for the full length between the trees and the tarp lays on top of it. Each type has advantages...but as I said, don't confuse tarp ridgelines with hammock ridgelines.