To put it as simply as possible, a facility based service means the client comes to your office (or facility) and a field based service means the professional goes to the client (or out in the field). One example of this in the health care industry might be physical therapy. A facility based physical therapy company would have an office or medical facility where the patient would attend therapy sessions. A field based physical therapy company would come to a patients home to conduct the physical therapy session. Below is a link to an example in the information technologies field. In these links, field based service is referred to as non-facility service.
It is as simple as working in the office/hospital or going to patient. Physical therapist can choose either of those job options or a combination of them, mett some patients in the office/hospital and see others at their home. Other than that physical therapist can work in a variety of non hospital environments. You can see degree description for physical therapist for more information.