Linear makes each player experience the same events each time they play the game. It is experience like the one in a book or a movie.
In a branching narrative what events a player experience depends on previous actions. It's a bit like a old Choose-Your-Own-Adventure book. If each branch was totaly seperate one would end up with alot if uniqe events. One way to solve that is a foldback structure where the branches eventually all lead to the same place.