Like so many common verbs, the meaning of "know" in the Bible is varied and dependent on context. And in some cases – when it is connected to ideas or objects – its spiritual meaning and natural meaning are essentially the same.
It's interesting, though, that when the Bible talks about people knowing each other and especially when it talks about the Lord knowing people, the meaning has more to do with the states of love within people than it does with any factual knowledge.
This makes sense if you think about it. When we really "know" somebody, what we mean is that we know what kind of person they are, what their motivations are, what they love, what they hate, what makes them tick. Those things are far more important than knowing their parents' names, where they were born or what year they graduated from school.
Most often then, especially applied to people, "knowing" has to do with the perceptions we have about other people's loves and the conjunction that can exist between those with similar loves, not just a collection of facts.