Periscope is Twitter's live-streaming video app that enables you to watch and broadcast live video. It can be downloaded for free from Google Play or the App Store. You will need a Twitter account to use it and you can connect the two accounts by logging into Periscope via Twitter.
You can generate your videos on iPhones and iPads and they can be viewed on any device via the app or on the Twitter website. You can watch videos or browse live streams by tapping the TV icon on the app interface. Periscope saves your video streams once you have finished creating them so that any Twitter user can view them for up to 24 hours.
You can choose to subscribe to the Periscope broadcasts of those Twitter users that you follow (if they are using the app) and you will be notified every time one of them starts streaming a video. Once you are watching a video you can then text the owner and other watchers. You can also like videos/streams by tapping the Heart icon on the app interface.
Before you begin broadcasting, you can choose to limit the video's audience using the People icon on the app interface. You then tap the Shoot icon, enter a title for your video and press the Twitter icon to promote the stream via your account so it is very straightforward to use.
Barbara Schroeder has blogged about potential educational uses for Periscope and this is available here. She also comments that there are some issues including generating poor quality videos and problems with school internet filters that can render the videos unusable. You may also run into problems with school policies on using videos of your students in the wider public arena so think carefully about what you stream. If in doubt, don't.