The White Tree of Gondor was brought to Middle Earth by Isildur after the fall of Numenor. He stole a fruit from the previous tree and planted it in the City that it now known as Minas Morgul. When the City was taken over by the dark forces, another sapling was taken to Minas Tirith. When the line of kings failed, the tree slowly died, but it had not produced fruit for many years. No new tree was planted until the coming of Aragorn and the Return of the King.
The tree in Numenor was a sapling from Telperion, a tree of silver light created by the Valar and loved by them and the Eldar above all else. The sapling was given to the Numenoreans by the Eldar as a sign of friendship between men and elves. When the men of Numenor began to turn against the Eldar, Isildur stole the fruit to protect the tree and its sacred heritage.
Although the tree has an ancient history in Middle Earth and Valinor, during the time of the Lord of the Rings, it is generally understood as a symbol of hope, and of a new beginning. In the movie, this is portrayed through the flower blossom which appears when Aragorn arrives at the White City.