what kind of; what sort of
Asks about the kind or type of something, like English 'what kind of'.
Use どんな to ask about the category, nature, or characteristics of a person, thing, or event. It always precedes a noun, and the noun is the object of the question. Think of it as 'what kind of ~?' For example, if you want to know someone's taste in music, you'd ask どんな音楽が好きですか?
Note that どんな is different from どれ (which one) or どの (which + noun). どんな is about type, not choice. For instance, どんな本ですか? asks what the book is like, not which book it is.
In conversation, どんな is common and neutral. You can answer with adjectives or descriptive phrases, such as おもしろい本です (it's an interesting book).