There are two Twitter-related cards. One of them shows popular tweets related to your query and it's only displayed for news-related searches.
The second card enhances Twitter results with recent tweets. For example, when you search for [nasa twitter], Google displays the most recent tweets, including those that were posted a few seconds ago.
Basically, Google has access to Twitter's Firehose API once again, 4 years after Google Real-Time Search was discontinued and Google+ was launched.
Twitter's blog says that "the desktop web version is coming shortly, and we have plans to bring this feature to more countries in the coming months." Right now, this feature only works in the US. "By deeply integrating Twitter’s real-time content into Google search, we hope you find it easier than ever to explore your interests across both Twitter and Google."
It's the end of the Google+ era. Even if Google+ will continue to exist in one way or another, Google will stop promoting it aggressively and will probably use it as a backend service. Bloomberg reports that Google "is set to reveal an online picture sharing and storage service that will no longer be part of the Google+ social network" and "will let users post images to Facebook and Twitter".