What does "Data error (cyclic redundancy check)" mean?

Before I answer your question directly, I'll say that you should not try to save a document directly from Word to rewritable DVD, or a USB stick, or any form of removable storage. It's one of the most common causes of data corruption in document files, and it can leave you no way to recover. Instead, always save documents to the hard drive, and then use the copying/burning software of your choice to write to the DVD (Windows Explorer in Windows 7 will do just fine).

Especially, do not open a file stored on removable media and edit it. Word uses lots of temporary files, and some of them are required to be in the same folder as the document file. Any sort of glitch in the data transfer can permanently damage the document. Copy the file from the removable storage to the hard drive, edit it there, close it, and copy it back to where it came from.

"Cyclic redundancy check" is a method for software to compare the source and destination copies of a file. The details aren't important here (they're at http://en.wikipedia.org/wiki/Cyclic_redundancy_check if you're interested). The message is telling you that what Word was attempting to write on the DVD wasn't accurately written there. That could be because the document itself is already damaged, or because part of the DVD surface is going bad, or any of a number of other causes. Just having written other files to that disk doesn't mean you can write this one, no matter what you name it.

One other thing, although you didn't ask: The reliability of DVD+RW disks isn't as good as that of DVD+R or DVD-R, which in turn aren't as good as commercial DVDs created by stamping in a factory. The reason is that in order to make the RW disks erasable, the dye that changes color when zapped by the laser has to be of a semipermanent type that eventually degrades or "wears out". The +R and -R disks use dyes that don't have be able to reverse their color, and they're more permanent. The stamped ones don't use dye at all, but a kind of metal foil.