Welcome back, 'user name here.' Please enter your password to continue. The most common form of 'Remember Me' seems to go something like this: This function is usually (more or less) safe on a public device while it shows the user name, the person would need to also know the password to access a given account. Alternative forms of this are 'remember my email' or 'remember user name', which makes it clear that they will need to enter their password again. Contrary to other answers, I would say that the password is almost certainly not remembered as a matter of practice.
'Remember Me' is typically used to remember the email address/user name of the user that logs in, so they only need to enter their password on subsequent visits.
