Broadly speaking, it's the ability to put yourself in another person's shoes.
She labeled parts of it “highly confusing,” she argued that I was taking her words out of context, and she stated that my motivation was to confuse her readers.
However, by putting my name on her website she generated a significant amount of attention for my essay, because within hours a horde of people googled my name, found the essay, and read it for themselves.
What empathy does is give you useful information that you can use to act on or not.
If you're talking to a classmate and know that if you bring up Subject A she'll be neutral, and if you bring up Subject B she'll get mildly annoyed, that's better than stumbling into the situation blindly.
The relationship will be better because with more validation you are going to have less debating, less conflicts, and less disagreement. When a person is feeling down, these bonds are sometimes all that another person needs to begin to feel better and solve their own problems.