The Idea:The 'Sufficiency of Scripture' (S-of-S) is simply the idea that the Bible is self-sufficient for "faith and godly living." Nothing more is needed to understand or apply it, everything you need to know about God is present and all the bits and pieces required for being a Christian are right there. Of course there is nothing about how to be an astronaut in the bible - but everything you need to know to be a faithful and godly astronaut!
Implicit in the S-of-S is also the notion of authority. In other words, the final authority of whose right and whose wrong about Jesus and our faith is in the bible. Again the idea of the S-of-S is not that the Bible is the final authority on skinning a rabbit, I imagine some fellow in Cygnet, Tasmania is the final authority on that.
One key advantage to this idea is security, provided God the Holy Spirit is in control of our lives, that we have all we need to be faithful. Our faith is secure, it is not dependant on the whims of scholarship or the shifting sands of opinion. God won't suddenly demand something more of us- or we won't wake up one day to discover being a Christian includes moving to New Zealand.