What are "Text format" option in standard Drupal?
"Full HTML", "Plain Text" and "Filtered HTML" are default Textformats in Drupal, they determine which elements are allowed in the input and what gets filtered. 

The wysiwyg editors only add UI controls to the field so user don't need to know HTML to style their output. If you don't want anonymous users to use formats like 'full html' you can turn it off in the permissions and give access to full html only to administrators or roles you trust.