We are told that Odysseus got his bow from someone he met in Lacedaemon. The man was named Iphitus, son of Eurytus. Odysseus traded a sword and a spear to Iphitus in return for the bow.
We are never really told very much about the physical appearance of the bow. Odysseus looks to see if worms have eaten its horns. And we know it has a centerpiece, where he rests his arrow, but we are not told anything more about it. The only thing the poet focuses on with the bow is how hard it is to string it, how only Odysseus is able to manage that feat.
The Great Bow of Odysseus is characterized by its immensity and power. It is extremely difficult to string the bow, never mind even shooting an arrow with it. In fact, Odysseus is the only person who has ever successfully strung it.
He got a long time ago from a fellow hero named Iphitus. It was special to him, but he didn't take it to the Trojan War with him. It rests on a peg in the treasure chamber of Odysseus's house. It also comes with a quiver full of bronze weighted arrows.
Although the bow is not described physically, we know that it is extremely powerful. It was always described by the epithet "great." It is small and lightweight enough that everyone is able to pick it up, even Penelope. However, its string is extremely tough and it is not pliable.