The Square Enix Account System is the site for creating and managing Square Enix Accounts and services associated with them. Originally launched in April 2009 to provide support for the Security Token in Final Fantasy XI and PlayOnline, Square Enix accounts are used for Final Fantasy XIV and the Square Enix Support Center, and will be used for Square Enix's future online services. In order to register a Final Fantasy XIV account, you will need to log in to your Square Enix Account at the account management system website (link below) and select "Add service" from the menu on the left side, and follow the on screen instructions.
In order to play FFXIV a Square Enix Account will be necessary. You can create an account any time by clicking the "Don't have a Square Enix Account?" button on the account management site. Once you've created your account, you can log into it on the account management site and you will need this logon information for any services which utilize the account, such as FFXIV. Once logged in, you will be able to access and manage your account, including doing things such as enabling various services such as the Security Token.
Your Square Enix account contains the options and settings to register a FFXIV service account, and additional characters or retainers. You can choose to register a credit card for payment, or pay for your account fees and services using Square Enix Crysta, Square Enix's "points" which can be obtained via Paypal or Ultimate Game Card, without the use of a credit card.