We've got a situation where we've got two discussions on pretty much the same topic, and as a result the threads are starting to get very hard to follow simultaneously.
The essence of this discussion, as spietreser and lucy24 note, is that you've got to have a longer than usual meta description for Google to be able to use it in building the new longer snippet. Google appears to be rolling out these longer snippets on its own schedule.
The other discussion, started by Storiale, who's also posted in this thread, started before this discussion did and was apparently unaware of the new serp description format which had been implemented.
The discussion in that thread, though, suggests that Google is relying considerably on personalization signals and search history to generate the new snippets in the serps for pages that don't have long enough descriptions. Several posts in the thread discuss the likely personalization aspects in some detail.
Because of likely ongoing overlap, I see lots of possible confusion with no way to piece the two threads together. I'm going to take a chance that it's going to be more productive to continue the question as one single discussion, and that the incognito thread, which discusses personalization in many fairly detailed posts, is likely to be the simplest to build on. I'm therefore going to lock this thread and suggest that we continue the discussion in the other thread, here... Different serp description when logged-in vs incognito https://www.webmasterworld.com/google/4803418.htm
This is a difficult choice, I should add, because the question asked here about longer meta descriptions has the more general and forward-looking title... though, as lucy24 points out, the question actually is about the new longer snippets. I'll refer to this discussion in the icognito thread, and link back to it for reference, since this thread does contain some material not yet mentioned in the icognito discussion.