These are checksum files. The checksum generated by either of the two means (md5, sha1) is in those files; it is a numerical value which is calculated from the content of a file. Should during the download anything have happened to damage the file, then a checksum calculated on the downloaded file should give a different checksum.
When you burn the iso image to disk with, say, k3b, then it will automatically calculate the checksum (I think md5 by default), so when it is calculated and it is identical to the one you can download from or read on the website along with the file in question, then you can be sure you have the correct file and it is not damaged. If the checksum deviates, then don't burn it, download again. Theoretically there is a slim chance that a file has been tampered with, so if on consecutive downloads you always get the same wrong checksum you should contact the originator of the file.
Robin
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