The IFDB is a user-editable catalog of interactive fiction, starting from the earliest days of Adventure all the way to contemporary works. People use it to discover and discuss IF, and in particular, the showcase of stories on the twinery.org home page is based on data stored there. The one thing the IFDB is not, though, is an archive to store your work. It only contains pointers to resources stored elsewhere on the web.
Once you've published your work, you can submit it for inclusion in the IFDB by using the submission form. Most of the fields in the form are self-explanatory, but one that might seem confusing at first is the IFID. IFIDs are similar to ISBN numbers for books; they're designed to uniquely identify your work, no matter what format it appears in. You can find your story's IFID by opening it in the editor, then choosing Story Statistics from the story menu. The IFID is displayed at the bottom of the dialog.
Also – make sure to set Twine as the development system for your work! That way it will appear on the twinery.org home page. This list is updated once a day – and it shows a random assortment every time the page is loaded – so it may take a little for your story to appear in the rotation.