Blue goblin mail is made by using blue dye on goblin mail. Like all goblin mail, it is too small for players to normally wear as armour.
However, during the Land of the Goblins quest the player can turn into a goblin using a transmogrification potion to access the tribal areas of the Goblin Cave. While wearing blue goblin mail the player can enter the Ekeleshuun goblin tribe's area and pickpocket the Ekeleshuun priest to obtain the Ekeleshuun key required to continue the quest.
Blue goblin mail cannot be traded, and therefore has no value. It can only occupy space in the inventory or bank. However, the dye and the goblin mail are tradeable.
You are required to make blue goblin mail in the Goblin Diplomacy quest.