FastSum creates a checksum using the MD5 hash algorithm. This creates an (almost) unique digital "fingerprint" of the file. (It is possible in theory for two different files to have the same checksum, but this is very, very, unlikely in practice.)
Once this has been done and saved, you can check other files against the stored value, and FastSum Standard will determine if any error has occurred in copying or if two files both marked "Version 1.5" really are the same file.
FastSum Standard has many uses. The most basic is checking CDs - especially CDs you are shipping to customers - against the stored value to make sure there were no transcription errors. Another is controlling mislabeled versions of in-development software. A third is checking files which should "never" change (such as many operating system files) to see if they've been tampered with or infected with a virus.
The FastSum Standard interface is fairly sparse, and requires reading the help file to fully understand what's going on and how to get the most use out of the program, but since this is a fairly technical program aimed at more sophisticated users, that's not too much of a drawback.
If you are in a position where you deal regularly with archiving or distribution of files - especially files which may change often - FastSum Standard is worth checking out.