Zesty Zeal!
When we say that you can know Longfellow by his zesty zeal, we mean that the guy wasn't afraid to be super-enthusiastic in his poetry. This form of open enthusiasm eventually died out as modernism became more cool and ironic. In fact, many modernists made fun of poets like Longfellow for not restraining their emotions enough. A passage like this one can give you a good sense of what we mean:
Plates of bone with spines projecting!
Painted was he with his war-paints. (8.40-42)
Longfellow is actually describing a fish in this scene, but his exclamation points and overblown enthusiasm makes it seem as though the fate of the whole world rests on this fish. That's just the kind of enthusiasm that'll make a modern reader roll their eyes. But, back in Longfellow's day, folks weren't afraid to get really deep into their stories.