Mint can be set to alert you to various events such as upcoming bills, or low balances on any accounts. It can be set to alert you from the app, through email or by text message. In addition you can sign up to recieve monthly emails about your money and ways to improve your budget.
With very few exceptions, Mint isn't just syncing your data over, but is using your username and password to log directly into the bank website. Banks will not reimburse for any fraud or stolen funds that may result from this, or may use Mint as an excuse to not reimburse for charges or stolen funds that occur from other causes.