Unlike with traditional FM radio, HD radio transmits with it information on the song, artist and album you're listening to. The most recent iPod nano has a song tagging feature for its built-in, traditional FM receiver, though it relies on later syncing the device with iTunes to make sense of what song you tagged.
With HD radio capabilities built into an iPhone or iPod, theoretically you could set your device to search for a particular song title via HD radio information. You'd also be able to quickly tag the song for purchase and be brought immediately to the iTunes app.
With iOS 4's multi-tasking capabilities, most likely one would be able to listen to HD radio stations while performing other tasks, much like you can do now while listening to iTunes. While streaming apps like Pandora are popular and will have backgrounding capability, HD radio does one thing Pandora doesn't: it won't use up your data plan.
Of course, as with any number of the slew of patents Apple files for, there's no telling whether we'll actually see HD radio built into future devices.