Whats exactly confusing with it?
Its a saying for god sake, ie'' i'm seeing this woman'' its the same as saying ''i'm going out with this woman'' or are you actually looking for the words, Girlfriend, courting etc
Of course you could interpret as ''seeing this woman behind someones'' { see zorro post} but at the end od the day you need to know if its your bird, or a friend, the OFFICIAL word don't come into by the way, what OFFICIAL about it, you went to the pictures and held her hand etc