"Facility" has more than one meaning, as with many words. "Facility" can mean that something is easy to do, or that someone has skill or ability. "She spoke English with great facility." This means, "She had great ability to speak well." "Facility" can also mean, "a building, special room, etc. that facilitates or makes possible some activity." (Webster's New World Dictionary) So, a medical facility is a building or room in which medicine is practiced.