He was insinuating that she slept her way to the top.
Most memorably, Huffington urges the assembled luncheon group: “Sleep your way to the top. Four hours is not enough.” She is a big advocate of naps and of dreaming up ways to reshape the workplace that men have designed.
What does it mean?
As I see it, you either don't get to the top because you like to sleep a lot; or you get to the top through beds (fornicating).
EDIT:
I found this TED video where Arianna Huffington uses this idiom in a funny way.
Best Answer
It's intended as a form of wordplay. As the comments note, to sleep one's way to the top is an idiom that means the trading of sexual favours for advancement of some sort. Although it can be applied to both sexes, it is usually an insult leveled at women who, correctly or not, are perceived as being unqualified for the positions they hold. (The stereotypical unqualified secretary, for instance.)
Given this context, the phrase can be seen as empowering for women who nap to increase their productivity. Stated plainly, it would be something like this:
The context includes "workplaces men have designed", so it's fairly clear that Huffington intends for her listeners to pick up the double meaning. She's basically saying, "Take that insult, embrace it, and make it backfire."
In some ways, it can be seen as analogous to the old joke:
You expect one thing from the sentence, and then when the full context is given, there's a shift in your perceptions. Huffington is doing the same thing with the phrase "sleep your way to the top".