David Toole has some comments about what that notion means:
An apocalyptic style is a way of acknowledging the strangeness of this biblical world and, by extension, the world generally . . . [apocalyptic style] founds itself not upon the identity of the same but upon the otherness of a world that never ceases to be strange. In this world, history continues not because of what kings and presidents might do but because ravens keep alive a prophet starving in the desert (1 Kings 17) and because even as kings and presidents count their people and take their polls and plan the future, the word of God comes into the wilderness (Luke 3). (Waiting For Godot in Sarajevo, 210)
Or, one might say that an apocalyptic style is a mode of doing theology which takes the utterly miraculous nature of biblical faith seriously. Of course, this can be a pretty embarrassing thing to do.