More campaigns, woot!
The campaigns in The Gathering Storm take on a similar approach as the ones found in the second Heroes III expansion "The Shadow of Death". In TGS' campaigns you take on the role of a particular hero in each campaign, and they finally unite to defeat a common foe in the final campaign. That's the extent of the story, I'm afraid.
There's also some new scenarios to extend the life of the game, but there was still no random map generator added which was disappointing. Still, the new scenarios weren't bad.
There's a new structure type (and a version for each faction) in The Gathering Storm, but those and the campaigns are all that's new in this expansion. If you didn't like Heroes IV, then stay away there's nothing of note that'll save Heroes IV in your eyes here.