There are three different tunics in the game. You start the game with the first one, the Green Jerkin, and you do not obtain the other two until much later in the game. Each clothing upgrade provides you with double defense from attacks, which is extremely helpful in the later dungeons.
 1) Green Jerkin
You begin the game wearing the Green Jerkin.
 2) Blue Mail
The Blue Mail is found in the Ice Palace. It reduces the damage you take by half (so, if an enemy were to attack you and do one heart's worth of damage when you were wearing the Green Jerkin, now he would only take a half of a heart).
 3) Red Mail
The final mail is found in Ganon's Tower. Once again, this halves the damage you take, making it twice as strong in protection as the Blue Mail, and four times stronger than the Green Jerkin.