Upon completion of the storyline from the original Disgaea: Hour of Darkness, you are given the option to start the game again with your character levels intact. In Disgaea: Afternoon of Darkness (and Disgaea DS), you are given the further option of starting with either Laharl or Etna as your main character. If you choose to start again with Laharl, you are essentially going to play Hour of Darkness over again, with your characters at their current levels. If you choose Etna as your main character, though, you are going to play in Etna mode.
The major difference in Etna mode is that Laharl is not available as a playable character any longer. For people that depended on Laharl in the Hour of Darkness portion of the game, this can be especially challenging. The story is completely different, but most of the battle stages are reused from the earlier portion of the game (with higher level enemies). There are three new battle stages towards the end of the story line.
The Etna mode is significantly shorter than the original story, though there are still plenty of things to do outside of the main story line. Additionally, most of the bills passed in the Dark Assembly in the initial play-through have been reset, meaning that extra stages unlocked previously will have to be unlocked again if you wish to gain access to them. These will also be significantly harder, and the set of stages available is slightly different.