The line from the rod and reel is tied to the ring at proximal end, and the line leading to the terminal tackles (the hook, lure and/or sinker) is tied to the other ring at the distal end.
This is particularly important for users of monofilament fishing lines that tend to express memory and form coils when released from a fixed-spool reel.
It is also noted that swivels can serve as weak points on the line, and therefore lessen the likelihood of landing larger or harder fighting fish.
[2] Fishing swivels, usually made of metal, come in sizes ranging from a few millimeters to several centimeters, and are traditionally either anodized black or brass in color.
It is somewhat possible that the swivel color plays a role in attracting fish, especially in low-light conditions.