"This hospital does not accept health insurances."
Translation:Diese Klinik akzeptiert keine Krankenversicherungen.
In (Australian) English, a "clinic" is usually a small doctor's office in a small town with only a couple of doctors working there.
A "hospital" is a large place with many buildings, wings and rooms, with lots of surgeons and doctors.
You go to a clinic (we call them GP's here in Australia) if you just want a general check-up or if you want to get a prescription for something. You go to a hospital if you've been in a car accident or you need surgery or something serious like that.