The primary purpose of Rama's avatar was to put down Adharma (personified by Ravana) and re-establish Dharma. Ravana has received a boon that he would never be defeated by a god or a demon. He looked so much down upon humans that he did not even consider including them into his wish. Therefore, Rama had to descend from his heavenly heights in the for of a man to take advantage of this loophole.
Here we see Rama holding a bow in his left hand, while the right is holding an arrow. Rama is a great archer, and archery plays an important role in many significant events of his life. Some of the episodes are:
1). His winning over of Sita by breaking down Lord Shiva's bow.
2). Ravana makes off with Sita while he is away trying to capture a deer with his bow.
3). His killing of Vali, the brother of Sugriva with an arrow.
4). The mere sight of him pulling an arrow from his quiver frightening the sea to give him way to Lanka.
5). His killing of Ravana by a special bow made by Lord Brahma.
When Rama broke Shiva's bow, he was given another bow by Parashurama, another avatar of Vishnu. This bow, known as 'Kodanda', is one of the few things Rama takes with him to the jungle. Images of Rama, such as this, leaning on his bow are known as 'Kodanda Rama'.