Snagit Chrome extension is what allows you to capture your screen. The Snagit Chrome app allows you to save your screen captures in your Google Drive account. You do have to install both the extension and the app for Snagit to work correctly.
TechSmith Snagit is currently in beta, you can register for early access here. Snagit will be released for the general public on November 19th.
Applications for Education
If your school is using Chromebooks, TechSmith Snagit could be a great tool for you. Snagit will allow you to create visual directions of how to use a website or Chrome app to share with your students. Being able to save your screen captures in Google Drive will make it easy to access and share your screen captures any time you're connected to the web.