If I specify 25 or fewer people to invite to a Hangout, they will receive a direct notification in addition to the post in the stream. Users who are signed in to the Google+ chat function when invited will receive an instant message with a link to join the Hangout.
One thing that is important to remember is that the Hangout you are in, and your participation in the Hangout, are visible to the Circles of other Hangout participants. That means that other people you know, and those you don't know, will be able to see that you are engaged in the Hangout.
Out of My Control
There are some things about Hangouts that I am not a fan of, and that could have privacy implications. Aside from the point mentioned above that my participation in a Hangout is visible in other Circles, it is also possible for anyone in the Hangout to invite other Google+ users to the Hangout.
If I start a Hangout with a select group of people to discuss something sensitive, I don't appreciate that any of those participants can bring others into my discussion without my consent or approval. Perhaps I want to discuss plans for a surprise birthday party for my wife, and someone I invite extends the invitation to their Circles--which include my wife.
What's worse is that there is no ability to kick someone out of the Hangout. So, whether it is someone I don't want to share sensitive information with, someone who is being belligerent or rude during the Hangout, or someone who is having audio or video technical difficulties that interfere with the Hangout for everyone else, my only option is to leave the Hangout myself and go start a new one.
One interesting aspect of Hangouts is that it integrates YouTube. So, you can launch and view a YouTube video as a group from within the Hangout. While the YouTube video is engaged, the microphones of Hangout participants are muted, but you can text chat about the video in a pane on the left.
I have participated in a few Hangouts. Most worked just fine, but I have been in one that seemed to have serious technical difficulties. There was significant bandwidth lag going on--not just for me, but for all Hangout participants. I could see everyone, and hear most people, but when one person in particular spoke others could hear him, but I heard nothing. We quickly just shut that Hangout down because it was dysfunctional.
Based on the visibility to other Circles, and the lack of control over who is invited to a Hangout, I wouldn't use it to discuss any classified information impacting national security, but as long as you are aware of the privacy and security limitations of Hangouts, it can be a very useful tool.