What is master key vulnerability in android? What is master key vulnerability in Android? From looking at a few different sites, I understand that it is bypassing the authentication provided by signing of apps.

How can I detect an app is vulnerable to master key vulnerability. Can anybody please give an example?
You've already described correctly what that "master key vulnerability" is about. If your only source for new apps is Google Play, you're most likely on the safe side; danger from this seems to be restricted to side-loading via unknown-sources.

However: If you want to check whether your device is affected, there are several apps out there which promise to do this. E.g. Belarc Security Advisor describes itself as checking for several hundred security flaws known on Android (including the master key). If the check is "positive", there are also fixes available, like Master Key dual fix or the Master-Key Security Patch (a module for the Xposed framework).