CRC-Verified files are files that have been tested on file corruption. If you download a file, then you should always make a CRC-Check on it (provided, that a CRC-Code was shipped with the file), to prove that your file is a perfect match for the original file you have downloaded. If the CRC check of a file fails, that means that the file has been changed/that there were some transfer errors. As a result, the corrupt file (e.g. videos, zip, etc. ) might not be able to open/play or be of any use at all. If you have a corrupt file, you should either redownload it completely or request a Patch for it. (Text about Patching missing)
There are download programs (emule/edonkey/bittorrent) that already have a file verification built in. Bittorent for example immediately checks each downloaded chunk for CRC-Correctness - if it fails the Hash-Check, then that chunk is redownloaded automatically.