Armor is one type of item you equip to raise your defense and defensive status (more defense to piercing attacks, basic, shadow, ect.). The 3 types of defensive items are Shields, Helmets, and Armor.
Defence
Defence protects your from damage. there are 4 types of damage: Standard, Piercing, Elemental, and Shadow. Defence reduces the damage you take from select types of attacks.
Resistance
Some armor have Resistance. Resistance protects you from status ailments. There are 7 different status ailments: Stun , Fire, Freeze, Shock , Poison, Curse, and Sleep. The resistances can be either positive or negative. Positive resistances help prevent status ailments, for example, resistance to fire or to frost. Sometimes there are also negative Resistances that allow more vulnurability to fire or frost or other status effects, but these are commonly found if there is another positive resistance.
Traits
Some armor have specal traits that affect you character other than Defence or Resistance. Some armors can increas your max HP or decrease the time bombs have to charge. some can even affect you in negative ways like lowering your attack speed.
Why are they so essential?
Because they defend you from much damage; With low quality armor, a high level enemy can easily kill you! That's why they are just as if not more important than swords, guns and shields. They also look really cool.
Different Armors
There are many armors based on monster, ie. he Snarbolax coat, but some monsters DON'T have a coat based on them(ie, Frostifurs) and some coats are based on monsters that don't EXIST(ie,the dusker coat).