The significance of app stores in mobile technology distribution lies in their role as centralized platforms for users to download and install applications. They streamline the process of finding, purchasing, and updating apps, while also ensuring security by vetting the apps before they are available to users. App stores also provide developers with a marketplace for their applications, which can lead to increased visibility and revenue through in-app purchases and subscriptions. Overall, they have transformed the way software is distributed in the mobile ecosystem.