what do people mean what they talk about dancers having facility?

Facility is the innate ability to achieve certain dance positions such as a 180 penche without much effort. It is being turned out at the hips and being naturally flexible. One can always increase their facility with training, but a professional needs the kind of facility that you must be born with and then trained to go even further.

Artemis didn't deserve a TD for her answer. It is pretty much the same thing I said.

Generally speaking, it means making something look effortless and easily performed. Alternatively, it can mean readily complaint (muscles, etc). It depends on the context of the word.