Paths tool is a vector path line which can be edited. Press B to activate paths tool or choose tools → paths.
Once path is created it is visible on ALL LAYERS, its basically entity of its own not related to any of the layers. You can find paths from layers / channels / paths. Paths tab has its own layers which you can delete, create, name and turn on/off.
Paths tab layers work pretty much like layers in layers tab, get it? Good ;)
If you want to hide path line, create empty layer in paths tab.
Paths vector line could be easily used to create very nice ArmA 3 or Farming Simulator rivers, creek beds or roads.