SMTP Error Could Not Authenticate

In my checkout, when I press next to go to PayPal it works but in the delay I get a message flashing:

SMTP Error Could Not Authenticate
SMTP Error Could Not Authenticate

then it redirects to PayPal ok.

How do I fix this?

You can that error because the SMTP configuration you have in the "email" area of the joomla configuration is not correct.
Please contact your hosting to company in order to check your SMTP credentials and put the correct information there an it will work.