The Combo Branch effect changes the number of branches in the combo map. The default number of times you can change a branch is 1 so Combo Branch +1 would result in 2 new branches off the branch path you chose, which will allow you to change paths 1 more time. A further addition would result in 2 new branches off that branch, and so on.
That extra branch may be more desirable because it is shorter, or because it is still available even after you accidentally missed a turn, or because it contains a symbol that is not available in other branches at all.
Note that you see only 3 branches on the screen at the same time. Therefore, you will not see the extra branches until you move up or down as appropriate.
It is always better to increase the number of combo branches (unless there's some weird side effects that we don't know about).
However, some items reduce your combo branches, but increase your statistics dramaticly.