"Jaki" asks for an adjective. To ask for an adjective in English, you usually use "what" at the start and "like" at the end.
His parents are <nice>. → What are his parents like?
"Jacy" is masculine personal nominative plural form of "jaki", formed according to the rules of adjective declension.
Only if it wasn't about people. Asking “How is the film?” is the same as asking “What is the film like?”, and I imagine both would translate to „Jak jest film?”.
But since the sentence is about people, “How are his parents?” means asking about how their life is going or how they are feeling lately, the same as “How are his parents doing?” or “How are his parents feeling?”
That said, “How are his parents?” could mean asking what they're like, if the surrounding context made that clear. So it's not ungrammatical, just unable to have that meaning when standing on its own.
After reading all the comments, I remain unclear. Is this sentence, in Polish, used to ask "what are his parents like?" ... (are they nice, mean, etc.) or is sentence, in Polish, used to ask "how are his parents doing/feeling"...are they well, ill, happy, sad. Or, is it interchangeable and can be used, either way? If the latter is the case, if I am asked the question, how do I discern what the person is asking ... what are they like vs how are they doing/feeling?
Wouldn't be better to translate it as "What kind of parents does he have?" At least for understanding purposes (in this comment section) to not confuse "to like". Though, yes, the more common colloquial question in english is "What are his parents like?" I am guessing the problem here is that english speakers are forgetting that we use the word "like" for describing in metaphors.