The greenwood tree mentioned in the opening song in Act 2, Scene 5 refers to any tree in a forest that has green leaves. A greenwood forest has often been associated in English myths and stories with benevolent outlaws, like Robin Hood. A greenwood tree can refer to either an evergreen tree or even a deciduous tree during its green, leafy season. The color green itself is known to symbolize nature, life, and even fertility. Nature, life, and fertility are also associated with well-being, growth, and harmony because only that which is alive can continue to grow, be well, and be at peace. Since green is associated with life and fertility, the evergreen that is constantly green has become commonly known to symbolize rebirth or rejuvenation. Hence the greenwood in the play also symbolizes the life, fertility, and rebirths the characters experience.
The association with fertility is obvious enough to see considering that four marriages take place at the end of the play. However, the characters, like Robin Hood, also escape into the Forest of Arden at the climax of life's hardships and there experience happiness while some even experience rebirth.
Oliver is one example of a character who experiences rebirth. At the beginning of the play, Oliver feels such an immense jealousy for his brother Orlando that he denies him the thousand crowns their father left Orlando in his will, plus denies Orlando the gentleman's education also promised to him in their father's will. In short, Oliver treats Orlando very poorly and even threatens his life both through arranging for Orlando to fight the court's wrestler and through burning down Orlando's dwelling, but Orlando escapes into the Forest of Arden. Oliver then pursues Orlando into the forest with the intention of still killing him, but has a severe change of heart when Orlando actually saves Oliver's life. While walking through the woods, Orlando sees Oliver asleep under a tree and about to be killed by a lioness. At first Orlando starts to just walk away, but repents and fights and kills the lion, saving his brother's life and becoming injured in the process. Oliver is so moved Orlando has just saved his life that he repents his own jealousy and hatred and is newly filled with love for his brother. This dramatic change in Oliver can be considered a rebirth, the same rebirth that the trees in the greenwood forest symbolize. We see Oliver's rebirth described when, in answer to Rosalind and Celia's question if he was the brother Orlando saved, Oliver replies:
'Twas I; but 'tis not I.--I do not shame
To tell you what I was, since my conversion
So sweetly tastes, being the thing I am. (IV.iii.135-37)
Other transformations or rebirths take place in the play as well showing us that rebirth is one of the many things greenwood tree symbolizes.