This is a question that has come up more than a few times over the past month, providing the perfect opportunity for a FAQ post.  This explanation, from the internet, provides the most accurate and simplistic answer.

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You frequently see the word or phrase healthcare and health care but are unsure whether they are the same. Many people use them to mean the same thing but they are fundamentally different.

Health care as two words refers to what happens to a patient. Often, health care is a passive event: the provider kicks off and the patient receives. But health care should be more like the full football analogy: after the Provider team kicks off, the Patient team runs with the ball. Health care should be an interactive event: both sides do something. Passive or interactive, health care as two words refers to actions by people who work in healthcare and by patients.

Healthcare as one word refers to a system or systems to offer, provide, and deliver health care (two words). Thus, the USA has a healthcare system. In Great Britain, they call it the NHS (National Health Service). The thing that doesn’t work well for anyone; that costs too much; has frequent errors; and too few providers, that is called healthcare.

Health care – two words – refers to provider actions.
Healthcare – one word – is a system.
We need the second in order to have the first.

(Source: Dr. J. Deane Waldman, MD.)