What follows is my summary and understanding of what Nietzsche was trying to say.
The story starts with Zarathustra finishing a decade of meditation in the mountains. He now feels the need to tell the people what he's learned. So he sets out on a journey back to civilization.
Lo! I am weary of my wisdom, like the bee that hath gathered too much honey; I need hands outstretched to take it.On the way back, he comes across another hermit. Only this one is focused on worshipping God in the wilderness and advises Zarathustra try nothing more among the people than making their lives a little easier, since they distrust sages otherwise. Zarathustra leaves the hermit on friendly terms, but secretly thinks poorly of him for bothering with the idea of God.
When he does reach the people in the marketplace, he begins to tell them about the 'superman.' This is a challenge to the idea that humanity is already the perfect pinnacle of living creatures. It's a condemnation of such vanity. Instead, Zarathustra believes humanity is — or can be — only a stepping stone to something greater, something better than mankind.
All beings hitherto have created something beyond themselves: and ye want to be the ebb of that great tide, and would rather go back to the beast than surpass man? What is the ape to man? A laughing-stock, a thing of shame. And just the same shall man be to the Superman: a laughing-stock, a thing of shame.But humanity's complacency and false religious disdain for the natural world threatens the chance of producing the superman. As the hermit predicted, the people in the marketplace weren't interested. They just wanted to be entertained by a rope dancer.
Zarathustra tries again to get his message across, using a rope dancer analogy. He gives a Beatitudes-like speech about the virtue of humans who devote themselves to being part of the rope bridge to the superman, or being raindrops heralding the thunderbolt of the superman to come. And he warns against humans who might instead become 'the last man': content, timid, and a dead-end.
Alas! there cometh the time when man will no longer launch the arrow of his longing beyond man--and the string of his bow will have unlearned to whizz!
I tell you: one must still have chaos in one, to give birth to a dancing star.
It's a bold vision, but low on the details. I do find it strange how often I've heard Nietzsche accused of arrogance or chauvinism, when he's pretty obviously preaching against human arrogance and chauvinism. He's the one suggesting we aren't — or might not prove to be — the pinnacle of living creatures.