A branching story splits into different paths depending on what the reader chooses, and those paths lead somewhere different. The definition sounds obvious until you notice how many stories branch and then quietly rejoin.
Branch, loop and gate
Writers talk about three patterns. A true branch splits and stays split, which doubles the writing at every choice and is why it is rare. A loop offers a choice, plays a different scene, then returns everyone to the same next chapter: common, and not dishonest, since the scene you got was genuinely yours. A gate is a choice that only unlocks something if you have paid, built up the right relationship score, or picked the matching option three chapters ago.
What this means for a reader
Count endings, not choices. A story advertising hundreds of decisions and two endings is mostly loops. A story with twelve endings is branching somewhere real, whatever it says about choice counts.
The second signal is memory. If a choice you made early is referred to much later, the story is tracking state, which is the expensive part and the part that makes a reread feel different.
Where branching costs money
In app libraries the branch is often the paywall: the free path exists, and the interesting one costs coins. That is a commercial decision rather than a narrative one, and it is worth knowing before you start a long story, because the cost compounds chapter by chapter.
Spotting a loop in two minutes
Make an obviously wrong choice early, keep reading for a chapter, and see whether anything refers to it. If the next chapter opens the same way it would have anyway, you are in a loop. Do it once at the start of a long story and you will know what you are buying for the next two hundred chapters.
See also choice-based story, cliffhanger paywall and the glossary.