If they don't, the email threatens, they will be considered to be fraudulent users and their email account will be shut down.
Unfortunately, there are always some users who will fall for the scam, and will follow the offered link to a spoofed Google login page.
The login details they will enter in this page will be harvested by the crooks behind the scheme, and either misused by them to compromise the accounts and send out spam from them, or sold to other criminals that will do the same.
"Phishing scammers often try to trick users into submitting login details and other personal information by claiming that account details must be verified to improve security," warns Hoax-Slayer.
If you are worried that this or a similar email might be legitimate and you might lose the account, please refrain from following the offered link, and access your account the usual way - via a bookmark or by typing in the correct address for the login page in the browser's address bar.