A quiver is a receptacle for holding arrows, and these useful arrow holders have been in existence for millennia. In archaeological records, anywhere you find use of arrows, or sometimes darts, you’re likely to find some variant of quivers present too. Early quivers that have been found were typically made of different forms of animal hides, cloth, or sometimes carved out of light wood. Most have some form of strap, though there are quivers that can be set stably on the ground too.
Size of a quiver may depend upon what type of bow you’re using, how many arrows you need to carry, and the size of the arrows. Choices of material need to be strong enough so the material isn't pierced by arrows, which are typically placed tip side down in their holder. On the Internet, there are even guides to making your own quivers out of cloth, though the majority of commercial quivers used may be made of light plastic or leather.
The arrows in the quiver need to be accessible so that a person shooting a bow can quickly extract an arrow. This usually means that the quiver has an open top, but is seamed or closed on the bottom and sides. Since many of these arrow holders are worn in some fashion, they often feature comfortable straps, which tend to come in three forms.
A double strap quiver may be worn like a backpack, with the archer reaching backward to extract arrows. Some quivers fit on the hip, and may be worn attached to belt loops. Others fit to one side of the body. Arrow holders that can stand on the ground can be used in competitions, with the person reaching forward to grab another arrow. These have been used in warfare in the past too, though someone had to set up the quivers, for which there wasn’t always time or room.
There’s a lot of debate about how many arrows a quiver should hold. Generally if you are walking long distances without being able to retrieve your arrows you’ll want to carry several arrows, perhaps a dozen or more. On the other hand, a higher number of arrows, especially if you’re walking or backpacking, means carrying more weight. Some people argue for carrying fewer arrows than a dozen. In archery competition settings, you may be limited to the number of arrows you can carry, or a standup quiver is filled with the number of arrows you’re allowed to use.