Within a hybrid mobile app built with Telerik Platform you may consider using the popular local storage type SQLite. This is achieved through a Cordova plugin which you need to install in your project.
Then you will be able to work with data locally in a SQL-like way. A demo for the plugin is available in the Telerik Verified Plugins Marketplace.
For more in-depth information and experience, I'd recommend that you try on your side the Telerik Platform SQLite sample app
As an integrated solution in Telerik Platform you may consider using the app Data layer. This will allow you to have an easy way of storing the data in a NoSQL cloud store and working with the data with a JS SDK and Kendo UI integration. With this approach you can save the data on the device for offline usage and sync it on demand with the cloud. This approach also allows for syncing the data between several user devices given their data is saved in the cloud storage.
For a quick way to start with using this solution in Telerik Platform refer to the Deliveries sample app
I hope that this answers your question.