Cave vines are generated in Lush Caves and they grow down from the ceiling. They have a chance of having glow berries. When bone meal is used on them, they will produce glow berries. To grow your own cave vines you will have to use (right click) glow berries on a block.
Cave vines in a lush cave (via screenshot)
Cave vines are found hanging from the ceilings in lush caves. You can collect glow berries from a cave vine by either using them (right-click) or breaking the vines.
Lots of cave vines hanging from the ceiling of a lush cave (via screenshot)
Cave vines don't have any use other than growing glow berries.
Cave vines are mostly for immersion and making the lush caves look more believable and authentic. You can grow glow berries from them and they provide some illumination.
A. Cave vines can grow up to 26 blocks in length.
A. You are able to pick up cave vines by using a shear on them.
A. You can increase the length of cave vines by using bone meal on them.