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New builds which include bugfixes can be deployed automatically and no upgrade is required - when this happens, just refreshing the page is sufficient to see changes. However, for major or minor releases, a manual upgrade is usually required. This page describes the process to perform an upgrade.
Within your app catalog, find the ListBurst app, and delete it by selecting Files > Delete Document from the ribbon menu. At this point, you will need to re-install the app.
During the period between removing the existing version and adding the new version, your webparts will not render. Do not attempt to remove or edit them in your pages. They will re-appear after the new app version is installed into the App Catalog.