"Ode to the West Wind" is an ode, or a kind of lyric poem that is meant to address a particular person or object, usually in an elevated way. A lyric is a relatively short poem that expresses a state of mind or way of perceiving the world. Shelley's poem is an ode because it addresses a thing, the West Wind; in effect, this wind is the audience for the speaker's thoughts.
Shelley's poem begins by exhorting the West Wind to listen to his poem. His poem is addressed to the West wind itself. The first three parts describe the wind in heroic terms. The wind is like an "enchanter" from which the dead autumn leaves flee; it is a "fierce Maenad," or female follower of Bacchus, the god of wine; it is what causes storms in the Mediterranean or Atlantic. In short, the West Wind is addressed as the personified primal force of nature. Each of the first three parts end with the speaker imploring the wind to "hear" him.
In part 4, the speaker wishes he could be ruled by the West Wind like the dead leaves. It's clear that he is in some emotional distress. Though he senses a kinship with the "tameless" West Wind, he is nevertheless "chain'd and bow'd" by the "heavy weight of hours," or his mortal existence.
In the final part of the poem, the speaker finally makes his request to West Wind: he asks it, "be thou me," and he asks that it "drive [his] dead thoughts over the universe," reflecting a desire to have his ideas spread like "ashes and sparks" throughout the world.