"Airhead" was the lead single from 1988's Aliens Ate My Buick (excellent title, right up there with Mars Needs Guitars, if you ask me (and you didn't)). The album was a bit of a style change for Dolby, and was more dance influenced that the synth pop that preceded it. As a result, his fans had a tough time with it. The album peaked at #70 (Dolby's last charting LP), but fell off the charts relatively quickly.
The video is a wonderfully creative, slightly eccentric puppet show. Dolby was (he probably still is) a visual artist; one suspects that he was involved in the design of the video. I haven't been able to find anything out regarding a specific target for the song, but he did marry actress Kathleen Beller in 1988. It is not too difficult to imagine Dolby finding inspiration for this song in the Hollywood scene. [By the by, pay attention to the the lyrics; they are truly great.]
As Dolby's popularity waned, he transitioned to film and video game soundtrack work, and I believe that he continues to work in the industry to this day.
Cool trivia facts (a bunch): Thomas Dolby's given name was Thomas Morgan Robertson; the Dolby nickname came from the keyboards and audio equipment that he used. Surprisingly, Thomas Dolby is officially a one hit wonder in the U.S. -- while "She Blinded Me With Science" peaked at #5, he did not have another top 40 hit. Lastly, Dolby played the keyboard intro to Foreigner's 1981 smash, "Waiting for a Girl Like You." (See what you can learn by reading the whole entry.)
In the interest of completeness, here is the link to the extended dance version of "Airhead," called "Airhead's Revenge," and featuring Salt-n-Pepa.