In the play Othello by William Shakespeare, the main villain, Iago, says many things hinting that he is not who he appears to be on the outside. Iago seems to be calm and kind, warm-hearted and loyal: many even call him "honest Iago," but there is a sting of irony to this -- Iago isn't honest at all. It is just a facade, put on to fool those around him into trusting him and letting their guard down long enough for him to trick them. On the inside, he is a cold and calculating genius, whose sole purpose in life is to achieve power and success -- through any means possible.
The phrase "I am not what I am" (I.I.69) basically translates to "I am not what I appear to be," but it goes much deeper than that. If you are not what you are, that what are you? It's really a paradox: a person can be one thing in appearance, but the interior can be starkly different.
Iago is never what he appears to be, taking on a chameleon-like ability to cahnge his character to suit a situation. Later, he virtually wishes himself into nonexistence when he says "Men should be what they seem, or those that be not, would they might seem none!"(III.III.148-149). Iago's hypocracy has a bit of foreshadowing to it: here is a man who is not what he appears to be, he tricks people into thinking that he is something he is not, and through his cruel shceming, he brings about his own downfall.
"I am not what I am" also has some biblical connotations to it. In Exodus, 4:14, Moses asks God what name he should refer to him as to the Pharoah. God's response is, very strongly, "I AM...