In the short term, the ions produced by an ionic hair dryer help reduce static electricity. Ordinary blow dryers tend to produce static electricity. Having extra charged particles (ions) in the air allows any built-up electrical charge (static electricity) to be transferred through the air to other nearby surfaces. This doesn't have much effect, since the "frizzy" effects of static electricity fade within a few minutes anyway. Coating the hair with gel or some kind of conductive conditioner would have a much stronger and lasting effect than ions, which only exist while the hair dryer is running. In the long term, ions are more reactive than other molecules, so they probably cause the hair and/or natural oils to be oxidized and the hair to become more brittle. But this is probably a smaller effect than the use of conditioners (good) or hot air (bad). More worrisome is that ionic generators generate ozone, which is good high in the atmosphere but bad here at ground level. Ozone contributes to smog and can cause lung irritation.

It sounds as if 'ionic' hair dryers are the same for your hair as ordinary hair dryers.

Here's the link for Good Housekeeping's review:

Here's some more from Good Housekeeping:
Ionic Hair Dryers
The Good Housekeeping Institute also tested a new breed of "ionic" hair dryers to see if they delivered. The dryers are supposed to bathe the user's hair in negative ions, which attach to positively charged wet hair, and lock in moisture. Testers found that the new dryers do not save much time, but they were helpful in adding sheen.

"You see a lot about ionic hair dryers these days," Levine said. "It's a buzz word. They are often billed as drying faster than standard dryers and often cost a lot more. We found mixed results, some faster, some slower."

Consumer reports say all hair dryers are called 'ionic' now:
Best hair dryers
Beauty on a budget
Last reviewed: January 2009
You can buy a hair dryer, also called a blow dryer, for $20, but surely a $200 hotshot with high wattage will dry your hair faster, right? Wrong. Despite big differences in price and wattage, drying time for the 10 hairdryer models we tested didn't vary much. Fancy claims were harder to assess. There were "ceramic" and "tourmaline" dryers among the high- and low-rated models. And all the dryers are claimed by manufacturers to be "ionic" (they release charged ions).