A file hash is a short string that represents the contents of a file. This string can be used to make sure the contents have not changed between the time the original file was created.
In general, simple CRC32 is fine when sending files to someone you know or when it isn't all that important to check for tampering or transfer errors. But in most cases you will want to use MD5 and SHA-1 hashing to be sure the file hasn't changed. For critical data, you may want to use SHA-256 or even higher.