This page controls three simple things:
Enable Customer Account
With this enabled, a customer will be able to log into the Accounts page, control their own customer data, and view their order history. Disabling this hides this functionality.
Require Customer Account
With this enabled, a customer will be required to create an a account with a user name and password on their first purchase. On returning to your store, they will be able to log in, and their customer data will be automatically prepopulated in the order form. Also, the database will not allow duplicate emails; each user will need to have a unique email. Disabling this feature will allow duplicate data in the customer records, and the customers will be able to select "Guest Checkout" and not be required to create or use a user name and password.
Show Remember Me Check Box
Enabling this will allow the users to set a cookie where their browser will store and "remember" their login information.