Nikon D40 and Tamron SP AF200-500 f/5-6.3 Di LD (IF)?

I just purchased a Nikon D40 with the 18-55 mm AF lense and a 70-200 mm AF lense. I would like to get another telephoto lense and have read the Tamron 200-500 is a great lense. My question is will the Tamron's Auto Focus work on the D40 or will I have to manually focus the camera? Also, in Tamron's literature it says it works with an APS-C size digital SLR. What does that mean? Also, the focal length is equivalent to 760mm. What does that mean?