Part of the idea behind universities
is that they exist for the public good
. They aren't just there so your kids have something to do after high school and to keep the mathematicians
off the streets. They exist to enhance the society that creates them.
Since the faculty are the primary inhabitants of the University, the theory goes, they should be a big part of this process. Unfortunately, for most, that's not the case. Rarely do University professors take an active part in public debate. A "public academic" is one that uses his or her position to raise the level of public discourse and bring their ideas to the masses.
In the 20th century, Albert Einstein was probably the best example of this. Besides his noted academic achievements, he was very active in the political discussion surrounding WWII and the Manhattan Project.
In the later half of the century, Noam Chomsky has been notable in this respect. He is a linguist but has made many political contributions and is widely read and respected.