I hope you already know how to enable the 2-Step Verification in your Google Account.
Application Specific Password is a type of security provided by Google, by which you can choose different passwords for accessing different applications. This service is mandatory for such applications, which can’t ask you the verification codes.
For Example : You can create separate password for accessing,
1. For accessing Google Services on Android, iPhone, or Blackberry
2. To Log-in to Android Market from your Mobile Phone or Tablet PC
3. To Sign-in on Chat Clients like GTalk, Aim etc.
4. To Log-in on E-Mail Clients like Microsoft Outlook, Thunderbird etc.
5. To Sync Chrome (between Android and Desktop), and so on.
To create application specific passwords,
1. Visit https://accounts.google.com/b/0/SmsAuthConfig?SetupComplete=1.
2. Click on “Create passwords”
3. Enter the name of Application for which you want to generate the password, and click on “Generate password”
4. Now your Application Specific Password is created, by which you can access that application without verifying a security code.
By using the above process, you can create a number of Application Specific Passwords.
To manage your application specific passwords (, you can visit https://accounts.google.com/b/0/IssuedAuthSubTokens, where you can Revoke or Add new Passwords.
You can also learn how to directly access the Google Account, if you have lost your phone number.