Android requires that all apps be digitally signed with a certificate before they can be installed. Android uses this certificate to identify the author of an app, and the certificate does not need to be signed by a certificate authority. Android apps often use self-signed certificates. The app developer holds the certificate's private key.
You can sign an app in debug or release mode. You sign your app in debug mode during development and in release mode when you are ready to distribute your app. The Android SDK generates a certificate to sign apps in debug mode. To sign apps in release mode, you need to generate your own certificate.
To Sign your App to relese it, Right click on Project, Go to Android tools, now click on export a sign APK and follow the process, If its first time then you have to create a new keystore and an aliasis into it, after that all process, Eclipse will give you a signed apk which is signed as release mode, Now you have to save that keystore file for later use like whenever you will update your apk then you have to use the same file to export new updated apk.
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-Aman