Merrill, the User Manual is both very well written, and very well organized. Your answer is provided clearly and in great detail there. Please see the link in my signature.
Essentially, Library Materials are edited via Kerkythea, utilizing the (free) Kerkythea as an advanced material editing studio.
Twilight allows you on the other hand to apply material templates to any texture/material except the "default" SU material so that you can quickly create many complex and advanced materials with no effort. Many of these materials are extremely difficult even for advanced users of Kerkythea to create, but you get them at the click of a button in Twilight with full SketchUp integration. These Templates can be edited via the Twilight Material editor to create 98% of the materials needed by architects. There are, on rare occasions, some materials needed that are not available as templates, in most cases they are already provided in very well done and free available libraries at Kerkythea.net downloads section.