Blaze rods are dropped by blazes when killed by a player. Blazes are flying mobs in the Nether that use a fireball attack capable of setting a player on fire for ongoing damage. They spawn from Blaze Spawner blocks in Nether Fortresses, usually found on upper levels.
You can also get blaze rods by putting two blaze powder plus a Minium stone into the crafting table, yielding one blaze rod. Intact, they can be used to make brewing stands and as a component of several items, such as Ender chests. Crafting blaze rods makes Blaze powder, which is an ingredient of several potions.
Macerating blaze rods yields 5 Blaze powder, which can be combined in the Minium stone to achieve Over Unity. In turn, 2 blaze rods can be converted into 5, simply by spending some EU on the rods.