Blazes are flying hostile mobs found in the Nether that are quite dangerous enemies. However, they are the only creatures in Minecraft that will drop Blaze Rods. These Blade Rod items are useful for brewing potions and for making Blaze Powder, another useful item. You might even be searching for blaze powder to craft Eyes of Ender and to ultimately find the End Portal.
Where to find Blazes
Blazes are located in the Nether, specifically inside of nether fortresses. These fortresses are generated randomly within the Nether, so you might have to do some exploring before stumbling upon a fortress.
When ready, enter the Nether Portal. Make sure you are equipped with health, food, armor, and weapons, as you might be in the Nether for a while. You will definitely be fighting mobs, so be prepared with powerful items.
Once in the Nether, you have some exploring to do. Because nether fortresses are randomly generated, they could be anywhere in here. Nether fortresses appear as large towers, bridges, and corridors.
In other words: be prepared to fight. As you explore the nether fortress, search for as many blazes as you come across. Specifically, however, you should be searching for a Blaze Mob Spawner. They are generated throughout the nether fortress and will help you farm Blaze Rods.
Note: If you are here specifically to later make Blaze Powder for the Eye of Ender Recipe, 1x Blaze Rod = 2x Blaze Powder.