Every time you change the password of your Google Account or Gmail Account, an email is sent to your primary and secondary accounts. Though most of us are always connected to the Internet, and receive the email notification but if somebody has changed your password, there are bright chances that email might get skipped.
Google is tightening up the security even further, and now it’s possible to get an SMS alert on your phone about password change or any suspicious login attempt Google detects e.g. Google Account getting accessed two different countries is one such example.
This setting can be found under the Notifications section of the Security section. The email option was already checked in for me, and when I selected the Phone option, I had to sign in with my password, and verify using SMS which Google sends it to the number configured. It is also possible to change the number here.
Remember this is only notification and you will have to take the next step of securing your account by using the recovery process. We recommend you to set up 2 step authentication for all of your Google Account. That way even if somebody knows your password, he or she cannot login unless you provide a security code using the Google Authenticator App or Code Received via SMS on your phone.