Go to Setup->Settings->Email settings, to check whether the SMTP is set properly, since all emails sent automatically are based on SMTP Service. Please click the Test button, if the test is successful then it can send email normally and then you can save the settings. 

SMTP setting is just like a door key in our system, after we wrote a mail, we need use this key(SMTP Setting) to open the door and let the SMTP service deliver the mails for us, if the key is wrong, we can't open the door.
After the SMTP is set properly, maybe there is another possibility, to check the Notifications settings, where you can make sure the required options are set and accordingly the system will trigger the emails as the corresponding events occurs.