This first installment of a two-parter introduced us to the animated version of Two-Face, one of Batman's most well-known villains. As Alan Burnett envisions him, he is terrifying, menacing, self-loathing, but fair in his own twisted way. Harvey Dent is troubled by his past, which he has suppressed so long that his bottled anger has created a second personality vying for control. Its heartbreaking and memorable television to watch his transformation, which culminates in a scene eerily reminiscent of the Joker's own transformation in Tim Burton's Batman film.
What makes Two-Face a great villain is his similarity to Batman. Both are well-respected and wealthy men in society. And both have darker personalities borne out of violence that have usurped their original personalities. Bruce Wayne no longer exists, and neither does Harvey Dent. The key difference, what makes the story so fantastic, is that they both have a moral code, but Batman's is based mostly within the law (a mix of vigilante justice and civil law) while Two-Face relies on the flip of a coin. This simplifying of a moral code to good or bad, live or die, yes or no (and leaving the decision completely to chance instead of calculated reason) is what makes him so evil and so terrifying.
Alan Burnett has written a classic episode that does honor to the Batman mythos. There are lots of allusions to the number two in the episode as well, if you look for them.