The black ash on your fireplace bricks is actually soot, which is essentially deposits of smoky dirt that have been baked into the brick by the heat. While ash could just be swept off of bricks, you'll need to make a bit more of a determined effort to get the soot stains off. It can be done, of course, and it is a simple process, just one that requires more elbow grease than would be called for were it simple ash stains.
Things You'll Need
Fill a spray bottle with warm water and spray down the soot-stained bricks before cleaning. This will help ensure the bricks do not just absorb the cleaning solvent.
Mix a cleaning solution of 1/4 cup all-purpose cleaner to 1 gallon of warm water in a bucket.
Dip a stiff-bristled brush in the cleaning solution and scrub the bricks vigorously until the soot stains start to come up off the bricks.
Wipe down the bricks with a clean sponge and rags. Rinse out the sponge and rags and repeat the process until the stains are cleansed from the bricks.