It's an idiom that involves memory and context. If you "can't quite place" something or someone, the thing/person is familiar, but you can't remember where it belongs, or how you know it.
Example: "I recognized the man, but couldn't quite place him." In this case, you know the man, but can't remember how you met him, or where you know him from. You might have met him at work, but if you see him in a store or at a restaurant, you might not remember who he is because you're not seeing him in his usual context.