The Blast Mask is given to Link by the Old Lady from the Bomb Shop
Location
The Blast Mask can be obtained by completing an entry in the Bomber's Notebook. You must complete the Old Lady entry in which you must wait until midnight for the Old Lady to enter town. Sakon the thief will attack her and steal her bomb bags. If you hit the thief with your sword, you will stop him from stealing the bags. Talk to the Old Lady and she will give the Blast Mask to you as a reward.
While it's not as useful as a bomb bag since it does damage to you, it is useful early on in the game when you don't yet have the bomb bag.
Uses
After obtaining the Blast Mask, it can be used to cause an explosion similar to that of a bomb. Equip the mask and the B button will change from your sword to an explosion. While wearing the mask, you'll be unable to use your sword so be careful when using the mask. With the mask equipped, hit the B button to cause an explosion. The explosion will cause damage to link (though this can be negated by raising your shield prior to the explosion). After the explosion, the mask will need to recharge and will turn transparent during this time.
