Beef that comes immediately from a farm and processed would be like chewing leather. Therefore, slaughterhouses and butchers who butcher sides of beef (supermarkets get box beef that is cut into primals) hang the sides in a controlled environment like a cooler for a period.
The standard period is about two weeks. During this time the pellicle forms and does protect the meat while the proteins break down.
Basically and frankly, aging means letting the meat rot in a controlled way.
If you go to the supermarket and see meats that are marked down because it looks greenish-gray, that is the aging process at work. That meat is actually better tasting and more tender because of the concentrated flavor.
Source: Cattle farmer and former supermarket meat cutter. I also butcher my own game.
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