Laying anchor off the shore of the island, most of the ship's company went to the island to restore provisions, repair the broken water casks, and find a tree to fell and replace the Dawn Treader's broken mast.
Not wanting to work, Eustace ran off to find a shady spot. Wandering off into the mist, Eustace became lost and found his way into a valley where dwelled a dragon. The dragon had only just come out of its cave when it lay down and died. Eustace went into the cave and found its treasure horde -- donning a rather lovely golden bracelet he found -- and lay down to sleep. When he woke up, he found himself in the form of the dragon. In a panic, he tore his way out of the valley and came down to the beach. The crew was about to slay him when he was challenged by Caspian and Reepicheep, who quickly deduced who he really was.
Working with the crew for a while, Eustace became disheartened in that he might have to remain on the island since he won't fit on the Dawn Treader. However, Aslan appeared to heal him and restore him to human form so that he could remove the bracelet, which Caspian recognized as belonging to the Lord Octesian. At the end, when the ship was ready to set sail, they decided that the dragon had either killed Octesian, or was itself the lord transformed.
"A powerful dragon crying its eyes out under the moon in a deserted valley is a sight and a sound hardly to be imagined."
C. S. Lewis ~ The Voyage of the Dawn Treader
This is what another writer made of the Story...
Eustace has little respect for others and lacks a sense of fairness: he tries to take more than his rightful share of water rations and lies about it, and later he slips away from his companions to avoid doing his part of the work. is behavior is beastly, and he turns literally into a monster, cut off from other human beings: he becomes a dragon – a creature straight out of the imaginative stories he had resisted. Only then can he begin to get outside himself, imagine how others see him, and “wonder if he himself had been such a nice person as he had always supposed”. After being un-dragoned by Aslan, he is able to escape the limited, materialistic, rationalistic world in which he had grown up, aided perhaps by Reepicheep’s stories about “emperors, kings, dukes, knights, poets, [and] lovers” who had fallen into distressing circumstances and recovered. Moral imagination comes to play an important role in Eustace’s life, and as readers respond to Eustace first with antipathy and then sympathy, they too can experience moral imagination at work in their own lives.