What is the purpose of the Dawn Treader?
Upon viewing the previous editor's answer, which is addressing the specific situations involved in The Voyage of the Dawn Treader, I would approach the question with a broader understanding of the entire Chronicles of Narnia as a series. It is important to understand the author's intent when writing the series as a whole, and then think about the possible purpose of The Dawn Treader.
It has been said that, "Lewis's most immediate and conscious concern in writing The Chronicles of Narnia was to write a really good story—to be, first and foremost, entertaining, while simultaneously possessing all those characteristics that great stories had in Lewis's mind—including myth, adventure, and far-off worlds which impact on our own". These aspects of myth and adventure were tools to create an effective allegory and tell an engaging tale. This allegory running through the entire Narnia series speaks of common themes from the Christian worldview and mythology combined; morality and truth, salvation and redemption, sacrifice, heaven and eternal life. These would be seen as the overriding principles the author was striving to represent through his characters and plots in Dawn Treader and the other Narnia chronicles.
Prince Caspian sets sail in the Dawn Treader to find the 7 Lost Lords that his wicked uncle Miraz had sent out to sea. The lords had been loyal to Caspian's father and so Miraz had sent them on what amounted to a suicide mission so that he could rule Narnia as he pleased. Caspian didn't know whether the lost lords were alive or dead, but he vowed that he would find them or at least find out what had happened to them.
Secondarily, during the reign the High King Peter, Narnia had possessed an impressive navel fleet and was known for it's epic sea voyages. Later, during Miraz's reign, the sea (like the woods) had become an object of fear. It was rumored that an evil talking lion (Aslan) lived on the other side of it and the "Narnias" wouldn't go near it. It stands to reason that, along with finding the lost lords, Caspian's voyage was symbolic of returning Narnia to it's former glory.