Tongue-in-cheek, campy, playful, moral, irreverent. Hercules never attempted to stay true to the myths (as if they are consistent anyway). It took a character who was hedonistic half-god with a legendary temper and turned him into a moral, positive persona whose sole desire in life was to help others. as the series progressed, he became a voice against the insanity and stupidity of American culture.
Nor did it take itself seriously. The series is filled with jokes at the expense of the heroes. The gods, portrayed as childish beings with immense powers, regularly use the most up-to-date slang and partake in unquestionably un-Greek activities (I distinctly remember one episode where a god surfs). They are designed to be laughed at, they act as though they want to be laughed at even as they show off their powers and insist that they are better than humans.
And the humans? Good or bad, as a leading character or an extra, behave like real people. They love and hate, they fear and gain confidence. They live real and simple lives, creating an environment that is believable.
The monsters and other special effects, terrible. I don't know if they were a product of low budget or were intentional, but in the era of a special effects explosion they added to the campy atmosphere of the show, as did the ridiculous fighting sequences (if I bounced like that fighting a real opponent I would be out cold before I landed).
Besides never pretending it was anything more than a light show with fun characters, it did have two elements I took from it. Hercules never confronts the gods and therefore the show never became about how strong and godly he was; he was allowed to remain a people's hero. Second, and more inspirational, the show followed him through loss after loss in his personal life. It was nice to see him get back up time and again so that he could get back to what he was best at - being a hero.
I loved the idea of a legendary/mythical character re-imagined. How would you feel about a similar approach with King Arthur, Beowulf, or an Asian character?