In other languages: 한국어.
Armour is one of the more important technological improvements you can start researching after first contact with the aliens. Even the first technological breakthrough in this area makes your soldiers much more likely to survive a direct hit on the battlefield, and decreases the amount of time your soldiers will spend recovering from wounds. It will help you build your agents experience much faster, and make the Battlescape somewhat more forgiving of mistakes and bad luck.
Coveralls - Light Kevlar protection that your agents will always have at minimum on the battlefield, although its not likely to help them much against anything other than friendly fire from the rifle or pistol.
Power Suit - Heavy plates with Elerium-powered muscle assist and air-filtering system, this will make your soldiers into veritable walking tanks, although still not invulnerable.
Flying Suit - Power Suit with Anti-grav harness allowing your soldiers to move more rapidly about the battlefield and negating the danger of some threats.
* Protects the wearer against all Incendiary/Fire damage, and 10% resistance to Stun damage.
** Protects the wearer against all Incendiary/Fire damage and the Stun damage caused by Smoke inhalation, as well as 20% resistance to all other Stun damage
Just like your soldiers, when one wearing armour dies, the armour's gone for good. So the only way to keep from losing armour is to keep your soldiers alive.
In addition, if you're unhappy with the performance of your soldiers and decide to have them sacked, be sure to remove the armour before doing so. If you do not then the disgruntled soldier will take the suit home with them and you will not see it again.