It is pretty common for users to forget their password. MantisBT provides two ways to handle such scenario: "Forgot Password" and "Reset Password".
"Forgot Password" is a self service scenario where users go to the login page, figure out they don't remember their password, and then click the "Lost your password?" link. Users are then asked for their user name and email address. If correct, then they are sent an email with a link which allows them to login to MantisBT and change their password.
"Reset Password" scenario is where a user reports to the administrator that they are not able to login into MantisBT anymore. This can be due to forgetting their password and possibly user name or email address that they used when signing up. The administrator then goes to Manage, Manage Users, locates the user account and opens its details. Under the user account details, there is a "Reset Password" button which the administrator can click to reset the password and trigger an email to the user to allow them to get into MantisBT and set their password. In the case where email notifications are disabled, resetting password will set the password to an empty string.