v.1. To develop or have many branches or tributaries: Once this tree reaches a certain size, it will begin to branch out. The river branches out into a great delta before flowing into the sea.
2. To grow out of a tree trunk or branch: I like to sit on a large limb that branches out from the apple tree.
3. To expand the scope of one's interests or activities into a new area or areas: At first I studied only Latin, but later I branched out and began learning other languages, too.