If you are looking at the back of an arrow then you will see the nock. This part is what holds the arrow in place when you are drawing the string back to its fully cocked position. If you wanted to look at it in the most minimalist way then you could cut the nock into the back of the arrow. This is not an effective and efficient method so most of the modern versions are separate from the arrow and are typically made from plastic. With the recent advancements in technology, there are also new forms of illuminated nocks
that make it easier for someone to recover the arrow after they are shot.
The nock that you are able to use depends highly on the arrow shaft that is used on the arrow. If the shaft is hollow then it is more than likely that you are going to be using a push in nock. If you are using a wooden arrow, or one that is solid then you are better off using glue on nocks. They are both good options, but they are not compatible with different shafts. The glue on version is the standard version and is generally made of plastic. They fit over the end of the shaft and are held together with glue or epoxy.
The push in version is made to be paired with the hollow shafts. There have been so many advancements in arrow technology that these have become the new standard. The arrows that are selling the most right now are hollow, so the nocks are increasing in popularity. They fit in snugly and allow the shooter to have a decent amount of adjustability because they can be rotated. The shooter cannot tune the glue on nock easily and it is going to be more difficult to change the nock if it is damaged.