How about a more simple explanation?
Let's say you have a picture of landscape and you need to fit it in a scrapbook-space that is smaller than the picture itself.
You can either:
A: Get out the scissors and trim off the edges to make it fit.
(OR)
B: Shrink down the picture so that it will fit in that space, keeping all of the scenery intact.
That's basically what dithering is... shrinking down the recorded sound and putting it in a smaller space without losing anything sonically.
If you don't have a CD-R that dithers, then you will truncate (or "lop-off") bits, which is just like cutting off the edges of your picture. Most of the stuff will still be there, but you'll be missing the true "full picture" of the original recording.
Truncating bits isn't always bad, but it's certainly not the ideal way to get the most out of your recordings. It takes away some of the clarity and detail when you truncate a 24-bit recording down to 16 bits.
Commercial CD recorders (..the kind you get at Best Buy and Circuit City) don't have the ability to dither... they will truncate your recordings. Pro-quality CD recorders like the Tascam CDR-700 (or the newer model CDR-750) automatically dither a 24-bit recording down to 16-bits and are a worthwhile investment if you are serious about recording music.