Denethor is such a minor character in The Two Towers that he didn't even make the theatrical release. So why talk about a character who's been relegated to the extended edition? Well, he still has an important role to play in the trilogy's finale, and Faramir's flashback gives us some good insight into what kind of man he is.
Denethor is Boromir and Faramir's father and, unlike most parents who have a favorite child but try to hide it out of a common sense of decency, Denethor makes his favor painfully obvious. He sees his younger son as weak and incompetent while praising his elder son's victory.
Just look at him: that long gray hair and wrinkled face with his large, sunken eyes. He looks as mean as his scathing remarks to Faramir make him seem. Soon, he'll learn that Faramir could have (and chose not to) delivered the Ring to him. Someone is going to get some spankings… or possible disowned.