Basically, the poem seeks to establish a relationship between the speaker and the forces of nature. In this case, the west wind is that force.
As a summary, the speaker addresses the west wind, asking it to listen to his words. He begins in stanza one by describing the helpful and powerful actions of the wind. These include spreading seed around the earth to grow into beautiful plants and flowers. In stanza two, the speaker reveals some of the more powerful elements of the wind, such as bringing the lightning and the rain. The third stanza reveals the power that the wind has over the waves and tides of the sea, concentrating on the tale of the Mediterranean Sea.
The fourth stanza changes a bit to include the speaker himself in the wind's actions. He notes that he would love to fly as a leaf in the wind and to be able to feel some of its power. He alludes to troubles and hardships on earth and yearns for the freedom he would feel with the wind.
Finally, the speaker asks in the last stanza for the wind to "make him a lyre" so that all tlhe world can hear his songs. He wants the wind to make him a voice of reason and prophecy for the world and to help him pull his fellow man from their fears and vices.
While literature is always open to interpretation, one of the key ideas here is the recognition of powerful forces in the world. The wind can be both devastating and nurturing, as the poem suggest. One might create an analogy here with God and spirituality. God is powerful as the wind, capable of spreaking bad and good. The speaker recognizes and accepts this power, asking to be a follower and disciple of it.