I am not sure what an app can do to me if it is able to discover my account, to what extent?
Thank you very much.
This permission is of moderate-high importance. This allows the application to read what accounts you have and the usernames associated with them. It allows the app to interact with permission related to that account. An example would be an app that was restoring your contact, would discover your Google account then send you to Google's login screen. It doesn't actually get to see your password, but it gets to work with the account. This is also legitimately used by applications to add contacts to your accounts, such as dialer replacements and contact managers/backup/sync/etc.
Its a huge security hole because it allows an application to add your facebook and google and other account names to your online profile without you realizing it. If the site is hacked the hackers could follow through to other know accounts if you were stupid enough to use the same password. Lots of people are that stupid so it will happen.
An online dating site or porn site might leak your real facebook and google account names to the people you are chatting with even though you never gave that information to the site itself.
Anonymous online? Not any more.