To me, a theocrat is anyone who tries to use legislative powers to enact as law the tenets of their particular belief system, thus restricting the rights of others who don't believe as they do.
Most obvious example: School board members, now thrown out, who tried to shove the "intelligent design" bit down everyone's throats in SCIENCE classrooms. It belongs in Religious Studies, NOT Science. Scientific theories are based on conclusions drawn from empirical evidence, with all effort dedicated to proving, DISproving, or expanding on them to make them into scientific fact.
Other examples would be trying to legislate the morality of others based upon one's own belief system. This, however, usually ends in irony, as it's the loudest bible-thumping screaming politicans who tend to get caught with their pants literally down with a transvestite prostitute...or involved in something else that'd horrify the most liberal, but SANE sorts out there in regards to "That's just GROSS" sexual proclivities.
Some people use religion as a way to try to understand themselves. Others use it as a bludgeon to beat others with to cover for the fact that they despise themselves.
The candidate who tried to run on the Constitution party was a theocrat, and a frightening one, defining that Americans must believe in his flavor of Christian scripture, that "this is what an American believes". Uh...no.
And a theocrat/neocon hybrid is the most dangerous sort, as they tend to use their belief system as an excuse for world-spanning political decisions. They're the modern incarnation of the Spanish missionaries, who thought they had a duty to go out and conquer lands, get the gold and convert the natives...by force. The least dangerous is one that just thinks this is all a black and white "second Crusades". The REALLY scary ones are the ones who could care less what happens in the long run, as they truly believe that these are the "end times" and think this is all to do with some sort of final battle, and they'll get hoovered out of their hot tubs in the rapture anyway.