While a quick Google search for the word gore will probably turn up as many pages about the former vice president, the most common definition concerns the sort of blood and guts you'd more likely find in a horror movie than at the White House.
Along with its step-sister splatter, gore refers to a particularly violent brand of horror movie, one where the moviegoer's satisfaction is measured by the quarts of blood spilled on the screen. The only inconvenient truth you'll find in gore films like the Hostel and Saw franchises is the fact that the poor, usually sex-crazed teen bastards who serve as victims will meet a decidedly sliced or diced end.
Recent gore films such as these have in fact raised the bar of graphic violence to such a level, some critics have labeled the films "torture porn". It's all quite "gory" to quote a phrase.
You'll find fans of gore discussing such works of art as Cannibal Flesh Riot on the blogosphere at sites like Oh My Gore, Castle Gore, and Terror Tube.