Air purifiers can work in one of two ways: by using a HEPA filter or Ionizer.
A HEPA filter is a super-fine filter that can trap airborne contaminants .03 microns in size. They work by sucking the air in the room into the device and pumping out clean air.
An Ionizer works by sending out negatively charged ions into the air that latch on to positively charged ions. This bond causes them to become to heavy to stay in the air and fall to the floor. The only problem with this is that you then need to sweep them up. Also, these ions can irritate asthma symptoms.
A HEPA device is more expensive. An Ionizer is cheaper.