From TV (esp Poirot) and movie adaptations. Also, anecdotally, knowing a couple of people who love her books, who just don't do problem-solving (aka "detecting"). Instead, they more enjoyed the setting and relationships. I surmised that she was popular for portraying the declining upper class as morally suspect to the growing middle class.
But I'm curious and happy to be wrong - which is why I asked. Do you have an answer?