What were the important ideas of the Sophists?
First and foremost, the Sophists were in revolt against the Pre-Socratic idea that there is some ultimate reality that is unlike what we perceive and experience in the ordinary world, but in some sense causes what we do perceive and experience. The Sophists elevated the importance of the world that appeared to exist for human beings, or as the twentieth century philosopher Jürgen Habermas (b. 1929–) famously called it, “the lifeworld” (although Edmund Husserl [1859–1938] originated the term). They all thought that virtue can be taught, which meant that anyone could participate in government, regardless of their wealth or social class. In that sense, the Sophists enabled ancient Greek democracy.
The Sophists insisted that moral beliefs should have rational reasons and be capable of defense in rational argument. In Sophistic treatments of morality, human nature was often opposed to society or convention, and the Sophists were on the side of nature.
Finally, it should be noted that the Sophists practiced in an oral tradition, which Socrates was to bring to a level of elegant perfection that no single philosopher or school has equaled in the millennia since his death.