Facilitation in the broadest sense means helping or enabling people to achieve a positive outcome. It's an important and often under-appreciated skill for designers and other UX professionals to gain. It's especially important as more teams embrace lean UX practices, which shift emphasis away from big deliverables toward facilitating outcomes such as continuous discovery and shared understanding.
Any kind of working session or meeting in which design decisions are being shaped needs a facilitator. The authors of Sprint, the popular book about running five-day design sprints, compare the facilitator's role to Brad Pitt's character in Ocean's Eleven: The facilitator "keeps the heist running." But you don't need to run a week-long workshop to benefit from facilitation skills.