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 hash was shipped with the file), to prove that your file is a perfect match for the original file. If the CRC check of a file fails, the file may have been changed or your file has been corrupted by the transfer. 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, via a tool such as ZIDRAV.
There are P2P clients (eMule/eDonkey2000/BitTorrent) that already have an inbuilt file verification. For example, BitTorrent immediately checks each downloaded chunk against the SHA1 hash in the metadata file - if it fails the hash check, then that chunk is redownloaded automatically.