- A CRC-verified file is a file for which the CRC has been found to be the same as a released 'good CRC'; it is very likely that the file is a good copy.
- A CRC-failed file is a file for which the CRC has been found to be different from a released 'good CRC'; it is very likely that the file is corrupt in some way.
If you've hashed a file for use it with ed2kdump, and AniDB lists it as 'CRC-verified', you don't need to do any further verification: the file is definitely uncorrupted.
A CRC is a form of file hash: a short representation of a longer file that is likely to change if the file is modified. CRC is a 32-bit hash, which means that the chances of a random corruption not changing the CRC are four million to one against. Many groups release CRC hashes of their released files, so you can make sure you've downloaded them correctly.
Any change, from a single changed bit to widespread changes throughout the file, will change the CRC. While a single-bit error is often imperceptible, files with major corruption may be unplayable. It is possible to patch a corrupt file to a known-good version using a tool such as Zidrav or QuickPar.
The other hashes AniDB lists (MD5, SHA-1, and ed2k) are stronger than CRC: the chance of a CRC differing between two files with the same ed2k, SHA-1 or MD5 hash is at least 79 billion billion billion to one. If the MD5, SHA-1, or ed2k hash matches a published 'good hash', then it is very unlikely indeed that the CRC will fail. When AniDB lists a file as CRC-verified, you can use any of the hashes listed to verify the file.