To answer this question, it best to turn to Shelley's beliefs. Though the son of a vastly wealthy family, Shelley's ideas were revolutionary for his time. He supported the ideals of the French Revolution, an event that filled most people of his class with fear and loathing. He aligned himself with radicals such as Thomas Paine, William Godwin, and Mary Wollstonecraft, whose daughter he married. He and his Romantic cohorts, such as Lord Byron, happened to be wandering around in Switzerland and Italy because in the Napoleonic War period, England swung right and held radicals like Shelley, who advocated for republicanism, women's rights, and Irish independence—and thought the rich should be solely responsible for paying the national debt brought on by war—in deep suspicion as potential traitors.
Within this context, and knowing that some of Shelley's writing, such as A Philosophical View of Reform, was blackballed and never published while he was alive, we can better understand the frustration expressed in this poem. Shelley knew he was right on issues that we take for granted today, such as the evils of slavery or the benefits of a wide franchise, but also realized his voice was being suppressed. He believed, as he wrote in A Defense of Poetry, that poets were the "unacknowledged legislators of the world" because of their ability to change people's hearts and minds with their words.
Therefore, we can understand how he wished his words, written on leaves of paper, could circulate around the world with the freedom of the autumn leaves blown around by the west wind. He longed for that unimpeded movement of new ideas. He wrote in his ode that he wished to:
Scatter, as from an unextinguished hearth
Ashes and sparks, my words among mankind!
Be through my lips to unawakened Earth
The trumpet of a prophesy!
These are revolutionary words. Shelley says he wants to spark a fire that will spread and awaken the people of the earth. He wants to "prophesy" to them, foretelling a better world that is to come. This will cause them to want change. He also writes that he wants "to quicken a new birth!" By this, he means he wishes to help promote revolutionary change. He asks finally:
If Winter comes, can Spring be far behind?
In other words, he predicts that the old order will come to an end. This is couched in universal terms but few would have missed what this meant.