The word "eloquently" conveys a sense of appreciation for the writer's skills.
Eloquence is the art of speaking or writing in a persuasive way, by resorting to literary devices for example.
If someone makes their point eloquently, it means that the way they express their argument, or convey emotion, is remarkable and skillful.
In fact, "The Dance" is one of Garth Brooks' most famous hits, having received several awards (including for its video), which goes to show its impact on the audience.
