That is referencing something, however, the context it is put in is crucial, so we have to find out what the context is first. The best practice when you need a good context and you don't have it in the current paragraph, is to go back one paragraph.
Let's do that in this instance, let's go back one paragraph. The first sentence already provides enough information to search for our context:
Sheryl Sandberg, chief operating officer of Facebook Inc., wants to change that,
We haven't found our solution here, but we do have a starting point: that references to something not explained in this paragraph. So let's go back another paragraph.
Our answer is in the last part of the paragraph:
Liberated women won the fight for education and the right to work at careers previously closed to them, but now, having deserted the green grass of suburbia for the grim concrete of the city, they’ve encountered a new obstacle: Few get a room with the view from the top of the executive suite.
This is a writing style to keep the text more enjoyable. If you keep in mind that the subject of the text is about femnism, you can piece together what the writer is trying to say, which is: "women don't get high-ranking positions as easily as men do." The book that is being talked about is designed to give women a better chance to get a job, by taking a perspective from a man's viewpoint as well. This makes it a lot easier to figure out your two sentences.
With this knowledge, let's look at them again:
“What am I doing that I don’t know?”
"What am I not doing that I don’t see?"
Personally I'd change the sentences to:
"What am I doing wrong that I don't know"
"What am I doing wrong that I don’t see?"
So in the end the two sentences are referring to how women should look at themselves and reflect how their behavior influences their position in the company. Why is that so? Because it fits the context it is put in, and by carefully analyzing the text.
Edit: As pointed out in the comment made by Em1, I overlooked a particular sentence. For the sake of completeness I will just make a new section to the existing answer.
She has written what could be called “The Male Mystique,” eager to shape female psychology in the mold of male power. “Lean In: Women, Work and the Will to Lead” is about how women must learn to act like men if they want to succeed in business.
This sentence gives a much better in-text definition than I gave and it requires less searching. After that, you can just repeat the last part of the original answers.
Once again kudos for Em1 for pointing this one out.