The free Gliffy Chrome app is an offline app. All diagrams created in the Chrome app are stored locally on your machine and not within Gliffy's servers. Please note, the Chrome app does not have all of the same features and capabilities as Gliffy Online.
Installing the Chrome App
The free Gliffy Chrome app can be installed from the Google Marketplace listing: https://chrome.google.com/webstore/detail/gliffy-diagrams/bhmicilclplefnflapjmnngmkkkkpfad?hl=en
Click on "Free", then you will be asked to confirm if you want to add "Gliffy Diagrams". Click "Add" to accept and install the app.
Opening the Gliffy Chrome App
Google gives you several ways to open up apps as noted in their help articles: https://support.google.com/chrome_webstore/answer/1054233?hl=en
You can find the item in the store at chrome.google.com/webstore, and click on the Launch App button, or use the Chrome App Launcher to open the app from your desktop.