For an interactive, data-driven website such as one built with Drupal, collecting and processing user submitted data will be exceptionally important. Most of this data can be captured using a web based form, i.e. a HTML structure with textfields and widgets for selecting different options.
Getting a form on to a webpage is easy, getting the user's responses is easy too, getting them securely is much, much harder. Drupal provides a standard, easy to use, easy to extend and secure way of adding forms to your Drupal website: Form API or FAPI for short.
This section of the handbook describes the different versions of FAPI and the different things that you can do using it (and what you can't do...yet!)