Releasing a Cordova app on the App Store and Google Play involves a series of systematic steps for both iOS and Android platforms. For iOS, developers need to ensure they have a Cordova project running on Apple OS X, build a deployable iOS project, open it in Xcode, and follow a step-by-step guide to sign and publish the app on the App Store. For Android, the process includes updating release information in config.xml and package.json files, ensuring proper building of the project, specifying platform-specific icons and versioning, adding the Android platform back, and signing the app using a build.json file. Once the app is signed and the final APK is ready, the last step is to upload it to the Google Play Store by following another detailed guide.