Can someone please explain what olduğunu or olduğu means and what context it should be used?  Thank you in advance! 

  ol + duk + personel suffix

  k ---> ğ

  ol  + duğ + u, un, um, umuz, unuz, ları

 Kim olduğun + u   biliyorum.

 I know [that] who are you.

That extra " u "  is required by the verb "bilmek". 

thank you for your help. The colour coding helped me make more sense out of it