Air injectors send water through an oxygenated air bubble. When ferrous (soluble) iron, sulfur and manganese particles come into contact with this air bubble, they're oxygenated, turning them into ferric (insoluble) particles. These particles can now be physically removed with a filtration media, such as birm or manganese greensand.
When the media bed becomes saturated with contaminants, the system will backwash, flushing the contaminants down a drain and replenishing the oxygen air bubble.