There are several different manufacturers producing so called "lumen nocks". They provide a small light at the end of the arrow. But why? Why would I need a tiny light on my nock?
They are usually used for making your arrows easier to find in low light / cloudy conditions. Also they give a certain flair if you happen to be filming your shot.
Imagine hunting in a forest, light isn't that great and it's hard to use a metal detector, and you miss. The idea is so long as you know the general area where it might have landed you will have a much easier time finding it.
Personally I think people just like gadgets and shiny things. I've never seen anyone using them.
Dynadin is correct.
Also, I would add, the arrows with fletching, broadhead tips, and tuning become very expensive. Losing a $20 arrow does not make sense when you can add $3 (per arrow) to the total price and have a much better chance of finding the arrow. As responsible outdoorsmen and women it is our job to take everything with us that we brought out, including gear.
The lighted nock also provides immediate feedback to the shooter, which is a valuable training tool. It is similar to tracer rounds in rifles and pistols in that you get a visual indication of the flight path. In archery you could use this to dissect what went right and wrong with a shot. With a lighted nock other people are also able to see your shot execution and help in the overall training.
I use lighted nocks on my arrows because it helps me judge the quality of the arrow strike on an animal. When the LED on the arrow tip flies across your field of vision, it leaves a trace in your visual memory of the shot. I can immediately determine if something happened during the shot, such as a deflection off a branch, or if the shot went true. On top of the extreme example of a shot deflection, I also have a memory of where on the animal the arrow struck. With information on shot placement, I now have a better idea of how lethal my shot was, such as whether it was likely a heart, lung, or double-lung shot, which may inform how I approach tracking the animal and how long I wait before trying to find it.
Lastly, I hope that my lighted nock disappears during the shot. If I see it run off sticking out of the animal, I know I had a shoulder strike or similar. All of these factors might change how I approach the next step of trailing the animal. If I didn't see the lighted nock run off with the animal, I usually find the arrow and I can asses the quality and type of blood to confirm the quality of the shot.
After giving me a lot of really good feedback on how well my shot struck the animal, the lighted nock then does the (less important, in my mind) job of helping me find the arrow if the arrow passed all the way through, or helping me find the animal if the arrow is still embedded. It is much easier to find a downed deer when there is a lighted nock sticking up.
Lighted nocks also have an advantage when shooting a traditional bow with an instinctual shooting style. The lighted nock can help you visualize the flight path of the arrow to develop your instinctual shooting at a faster rate because you are getting more feedback about not just where the arrow hit, but the path it took to get there.
I was a scoffer until I shot my first deer with a lighted nock after they became legal in my jurisdiction, and now I won't hunt without them.