"Branching points" refers to moments or decisions in life where one has to choose between different paths or options. It symbolizes a crossroad or a division point where one's direction or future can go in different ways. Full definition
You see how the thick branches point away from each other? (treehugger.com)
These lesions, which occur only in areas of eccentric thickening (ie, at branch points of the arterial vessel), are characterized by the addition of massive extra-cellular lipids that displaced normal cells and matrix. (strokecenter.org)
The form this trend often takes is toward features such as morality meters and discrete moral choices at key branching points in game narratives. (clicknothing.typepad.com)