If you're currently using 3rd party integrations or applications installed through update sets (including those from the Share portal), you've already realized that there's no way to know if and when the vendor has made an update available without checking with them. The ServiceNow app store will fix that. Since you will be accessing the store and downloading applications directly from your instance, there's no need to worry about manually installing update sets. You'll also see when there's an update to an application you have already installed.
The Applications module is your new home for developing, browsing the store, and installing application updates. We can see here that the CAVUTest application has an update available. We can also review the release notes provided by the vendor.
From what I can tell (at least in patch 2), there's no preview of what has actually changed in the application before you click update, like you could with update sets. So like most app installers these days, you're at the mercy of the release notes and any documentation that might be provided.
You can also view the list of recently updated applications from this page.
Once the upgrade has completed you can view some useful information in Upgrade History. This works just like ServiceNow delivered upgrades. It will show the number of inserts, updates, deletes, and skips as well as all of the detailed records and their disposition. Although in my recent tests it appears that everything that already exists is reported as updated even if it hasn't changed.
Next up we'll cover application dependencies, viewing changes you've made to an application, and uninstalling. Y'all come back now, ya hear?