PhD thesis defense - is there a separate defense session with one's graduate committee? I was watching a math PhD thesis defense on YouTube and it seems that after about an hour of the talk, a committee member tells the audience to leave except for the graduate committee and the PhD candidate.

What typically happens next?  Is there a separate defense session with the graduate committee?

For reference: United States
That varies from place to place, even in the US. Your advisor will give you the best advice. But yes, a private session with your committee is pretty common. They want to assure themselves that you are "seasoned" and have both the required depth and breadth to be awarded the degree. 

Again, your advisor will tell you what to expect, but it is possible to get questions that are unrelated to your thesis, or even to your specific subfield. In mathematics, members of a committee often have different specialties and may want to know what you can say about their own field as they may have only a sketchy knowledge of yours and of your thesis. 

Don't, in general, expect it to be just a presentation. The public part needs to be a bit less technical in tone, since many of those present are looking for an overview. That isn't enough, of course. You need to say what you did and the key ideas that got you there.