It's about opening up possibilities, rather than choosing a specific path out of pre-determined options. I don't know the series the quote comes from (but I 'know of it' and it's on my list of things to watch...) but from the context given, it means that you were on a "straight line" path (in a limited sense of what you are looking at) but then make a choice and it "branches out" from that path. Like when a new branch forms on a tree from the trunk you had already.
Out of your 2 options it is (A) but with the sense that all those "branches" of the tree don't exist already. They only come to exist when you explore a path by making a choice.
EDIT: I didn't get involved in the philosophical debates about this (in the comments) but do understand them -- but from the specific wording "Forks off into a new possibility" I would take it from context that a 'new' situation is being generated, that is "shooting off" (outwards) from the old one.