Mail protects well against cuts, though is weak in protecting the head and joints.
Also it is less strong against piercing and smashing attacks, but that is easily amended by supplementing it with a thick undercoat, which is quite good against those attacks.
Mail quality depends very much on the material, the weave density, ring thickness and also on the type of construction.
Riveted links are better than welded ones and welded links are better than than butted ones.
Almost all historical mail armors are riveted.
Several factors explain the popularity of mail:
It can be worn on most parts of the body, it protects the wearer reasonably well and is flexible to move in.
Also, it is easy to clean, by rolling it around in a barrel full of sand, which scrapes rust and filth off.
A weakness is that it is hard to repair.
Mail was so common that several words to describe it have settled down in history.
A "byrnie" is a waist-length mail shirt, a "haubergon" reaches down to mid-thigh and a "hauberk" down to the knees.
A "coif" is an extension of a shirt that covers the head like a hood.
Though a coif offers some protection for the head, on the battlefield soldiers usually wore real helmets over it.
Mail seems to have been invented by Etruscans or Celts, in Europe, somewhere in the 3rd or 4th century BCE.
The Romans, when they encountered it, quickly adopted it as one of their main armor types, the lorica hamata.
Other peoples did the same and in the course of a few centuries it had largely replaced the earlier scale armor.
Mail was a very popular type of armor for almost two millennia, especially in Europe and the Middle East.
In East Asia lamellar armor remained the dominant type.
In the Middle Ages, mail gradually gave way to plate armor.
War Matrix - Mail armor
Greek Era 330 BCE - 200 BCE, Weapons and technology