Curiosity can be a good thing, in fact, it is what drives our societies and our personal development.
But too much curiosity or ”the wrong kind” can be harmful to us. So my interpretation of this quote is to be wary, curiosity killed many a cats trying to cross the roads.
I interpret it as a note to take heed when it comes to curiosity. Not to take it too lightly, not to be naïve and make assumptions and take out victories prematurely.
Care might need to be taken depending on the situation and circumstances.
Having said that, the right amount and the thoughtful kind of curiosity drives us forward, and often leads to richer lives and better things, which is worth remembering also 🙂