From Kottke - who describes the significance of the clip thusly:
It's not just that Michelle Obama is the first black First Lady. It's also that she was born in 1964. She's sixteen-seventeen years younger than Hillary Clinton or Laura Bush. She was in high school when hip-hop broke. Even Barack was already in college. She probably did a few of these dances in a South Shore parking lot when her husband was already thinking about getting into law school. In Joshua Glenn's generational scheme, Barack is part of Original Generation X, while Michelle's firmly in the next cohort, alternately titled Generation PC/the Reconstructionists.
Michelle is the first First Lady of the hip-hop generation. And not only does that explain a few things; it's incredibly awesome.
More where that came from. And a special note: I've never heard of the Dougie, the original Beyonce song, or the Beyonce video they're imitating.
One more: Michelle is gorgeous, isn't she? I love her.