What is Brazilian Jiu Jitsu? (Answer unashamedly copied from Wikipedia :)  )

Brazilian jiu-jitsu is a martial art, combat sport system that focuses on grappling and especially ground fighting. Brazilian jiu-jitsu was formed from Kodokan judo ground fighting (newaza) fundamentals that were taught by a number of individuals including Takeo Yano, Mitsuyo Maeda and Soshihiro Satake. Brazilian jiu-jitsu eventually came to be its own art through the experiments, practices, and adaptation of judo through Carlos and Helio Gracie (who passed their knowledge on to their extended family) as well as other instructors who were students of Maeda, 

Which books do you recommend? (click on book title for amazon.co.uk weblink)

The book I always recommend is Jiu Jitsu University by Saulo Ribeiro great book with all the fundamental techniques

What sites do you recommend I check out? (click on website name for weblink)

Grapple Arts is a good resource that I used when I was starting out

How does grading work?

Grading is measured on a lot of factors including skill, attendance, competitions and other factors.  It is a long road in BJJ with the average person taking 10 years to black belt and then only at most 10% of people who make it to black belt.  This is definitely an enjoy the journey kind of art :)