Why would a protrunding branch block the view from the window?

I think you mean protruding, which means sticking out, usually in the way of something. So a protruding branch is a branch which sticks out in the way, which would tend to block the view from a window. Protrunding isn't a word.

A protruding branch would block the view from the window because the tree in front of your window may just have protruding branches and broad leaves, so the view of your window will be blocked.