Based on my knowledge of Russian and German (not necessarily Polish), I would say that "jaka" is probably a lot like "which" in addition to "how".
In this case, "co" would make less sense, then. Think of it this way:
"Co jest twója odpowiedź?" -- What is your answer? Well, it's an answer. Duh!
"Jaka jest twója odpowiedź?" -- Which (answer) is your answer? Well, my answer is [blah blah blah]....
In other words, the proper response to "co" is to identify what the thing is, and you've already specified that it's an answer. But you want to know which answer, and that information is requested by asking "Jaka?"
i am german, and you can say in german both, how but also what Wie ist deine antwort, was ist deine antwort. so it is again different from polish and english. in polish i think only jaka is correct maybe also która jest twoja opwiedz? but i think jaka is more like what is your question and która as mentioned above in a comment is more like which
Since Jaka is said to be a sort of an "adjectival what" that seems to require an adjective as an answer, does this mean that asking "Jaka jest twoja odpowiedź?" should be answered like, for instance: "good", "bad"? From the comments I've read here, it doesn't seem to be the case, so this sentence may definitely not be an exemplary (most common) way to use Jaka, no?
It is a very basic usage of "jaka", it's just that I've always had problems explaining this particular difference ("co" vs "jaki"). I guess that perhaps "adjectival what" is not the best possible name for it.
I found this old explanation from br0d4, even if there's an exception that I can't think of, this should generally work:
If in English you have "what" on its own (What is this? What do you want? etc.), then it translates to forms of "co" ("co" undergoes declension through cases).
If in English you have "what" and a noun/pronoun (What color do you like? What is your question?), then it translates to forms of "jaki" ("jaki" undergoes declension through cases and genders).