I love the perennial and basic questions.  This is another one.  Most simply, how well can we know another person.  A little more deeply phrased, how well can we know the mystery of the "other," given that we have so many varying traits or sub-selves.  And we are always "works in progress," never to be pigeon-holed for long.  If we accept the view that there is a core self, how well can we come to know it in another.  If we accept the view that there is no core, but only a series of sub-selves, varying with each situation, how can we ever claim to know someone else.  (See my question, "Are We One or Are We Many.")

There is a literature on the mystery of the other, quite lovely in its depth.  Recent psycholgical writing tends to emphasize that we underestimate how difficult it is to truly know someone else.  This contributes to the breakdown of marriage, it is suggested, as we keep changing, but fail to keep our partners apprised as to how.  So do we grow apart without noticing. 

Martin Buber in "I and Thou" puts this most sensitively, poetically.  It enters the realm of mystical knowing.  But not obscure knowing, just knowledge of the other seen as ends only, not just means.
You'll have to read the man to gain a sense of what these words mean; then you can tell me.