In this example:

Oh my goodness. It was so moving, by the end I was tearing up.

...the speaker started to feel moved by the book as she was reading it. As she got closer to the end of the book, she continued to feel more emotional. The phrase "by the end" explains that she didn't just suddenly tear up while she was reading the last few pages of the book; she slowly started to feel that way as she was reading it.