What does 'branching' mean in terms of setting/resetting bits?

In an interview, I was asked "How do you set or reset a bit?" This is a very simple question, and I answered it.

After that, they asked me how to do the same thing, but without branching. I don't know what branching is.

I search and found Bit Twiddling Hacks by Sean Eron Anderson, but I'm still not getting concept of branching and non-branching.