Unfortunately, the Internet can be a nasty place. There are several people that would love to do harm to your computer. This is where checksums come into the picture. If the computed checksum for a downloaded file does not match the one posted by the original author of the file, then it is extremely probable that the file has been tampered with. To ensure that all of the files you download are in their pristine and intended state, you should always verify them against the official checksums posted by the author.
Additionally, downloaded files sometimes become corrupt due to network errors during the download process. This is especially prevalent while downloading large files. Checksums come to the rescue again in this situation. They ensure that your file was not corrupted or truncated during the download process.
In short, if the checksums don't match, you don't want anything to do with the file. Try downloading it again, possibly from a different source.
Not all files that are available for download from the Internet are accompanied by checksums. In these situations, you should contact the author of the file directly and request one via e-mail.