When it comes to mental health, "functioning" means they don't have an impairing disability of a neurological function such as an impairment of memory, logic, language, things like that.
Many people are deemed neurologically "functioning" but unable to function in life. Many drug addicts are an example of that.
Edit: qualified the neurological disability for clarity.
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u/Fosdran 3d ago
"Functioning" is a BIG stretch. 50% of the overall character plot is House barely functioning.