First off, tripe is the stomach lining of a ruminant, used for food.
Often considered the best of all tripes, honeycomb tripe is the meaty and tender tripe from the second stomach of your friendly neighborhood ruminant, most often a cow (or bull. A head of cattle, if you like). When a recipe calls for tripe, this is almost certainly what it means.
Honeycomb tripe gets its name from its lining, a number of thin membranes, connected in a diamond pattern. Also found in the second stomach is pocket tripe, which is not as good as the honeycomb tripe, but better than the plain, or smooth tripe found in the first stomach.