How can I treat brick efflorescence?
Dilute white malt vinegar (a 50/50 solution) will remove it; apply it with a nylon brush dipped in the solution and scrub gently.  If you're outdoors, you could rinse the wall down afterwards with water.  If not, scrub it again using plain water.

The vinegar reacts with the lime leaching out of the bricks (which is causing the efflorescence) to form a different salt of calcium which (a) isn't visible and (b) is water soluble, so rinsing or scrubbing the second time should get rid of it.