Although this article is based on canonical information, the actual name of this subject is pure conjecture.
Hiccup's Fire-Suit is a suit that Hiccup Horrendous Haddock III wears to protect himself against fire. The Fire-Suit is made out of dragon skin. At the end of How to Steal a Dragon's Sword, the Fire-Suit became Hiccup's primary clothing, as he went into exile and a war started. After this, Hiccup usually wears his iconic fur vest over the suit.
The Design of the Fire-Suit is rather simple. It is made entirely out out dragon skin (species unknown), it has openings for the eyes (assumed something protects them, because Hiccup hasn't been burned yet), and it covers the entire body with two visibly distinct gloves.
As the name suggests, Hiccup's Fire-Suit's main purpose is for protecting him against fire. In How to Steal a Dragon's Sword, Hiccup wore the suit when he descended into the fire pit where the crown was hidden, and spoke to the Wodensfang for the first time.