They are for exercise and have been around for a little over a decade. I’ve mostly heard of them being used by football players and martial artists, but they might be popular among other groups for all I know. The name comes from the idea that the ropes are heavy and not easy to control at first, so you are doing battle with the ropes. In other words, the exercise itself might be called “rope battling,” and the tool you use is a “battle rope.” The creator also likes to say that the benefits of rope training “will transfer into your chosen battlefield,” by which he means whatever other physical activities you engage in. The battlefield metaphor is probably an extension of the name, though, and not part of its origin.