Tryambakam is a bow of Shiva. The story of Tryambakam bow is found in the Balakanda 66 sarga of Valmiki Ramayana.
When Sati self immolated in the infamous Daksha Yagna, Shiva in anger took the Tryambakam bow to annihilate all the Devas (demigods) who participated in the Daksha Yagna. Fearing total destruction of Devas then sang glories of Shiva.
Shiva soon took a peaceful form and gave the Tryambaka bow to the Devas.
Devas gave the bow to Devarata, who followed Dharma on earth and used to help Devas in their battles. Devarata was an ancestor of King Janaka.
The Tryambakam bow was so heavy that it was kept in an iron box which had eight wheels. The box was pulled by 5000 soldiers.
King Janaka had announced that only a person who picks up the bow and tie it will marry Sita. Many famous kings attempted to pick up the bow and marry Sita, daughter of Janaka. But none of them were able to even move it.
Sri Rama and Lakshmana who had arrived at Mithila along with Vishwamitra Maharishi desired to see the Tryambakam bow. With the blessing and permission of King Janaka and Vishwamitra Maharshi, Rama picked up the bow and as the bow could not bear the strength of Sri Rama it broke into two pieces. Sri Rama later married Sita.
Please note that this bow is also known as Pinaka.