A checksum is a string of characters which uniquely identifies a file, a digital fingerprint. Change even a few bytes of a file--for example, by infecting it with a virus or replacing an old version with new one--and the checksum changes. Marxio File Checksum Verifier (free/donationware) is a small, standalone utility which will generate a checksum for a given file and then compare it to an earlier value.
Marxio File Checksum Verifier is very simple in operation. Either drag a file to the window, or select one using a standard file dialog. Then choose a checksum algorithm, such as MD5 or CRC32. (If you're the target audience for this tool, you know what those things mean.) Then paste a checksum from a known version of the file into the bottom text box, and check! Marxio will quickly tell you if they match or not. (Very large files may take a while, but Marxio will run minimized and flash the taskbar when it's done.)
There are several uses for this program. For example, freeware programs are often distributed by many different sites--some not trustworthy. If you have a checksum of a known copy of a program, you can compare a downloaded copy to be sure you're not getting one with a virus or a Trojan. Checksums can also be used to validate that two sets of compressed data contain the same files, without opening each archive and manually checking the contents against each other.
There is not much more to say. There are a decent number of options hidden in the Options menu, including maintaining a history file and shell integration. Marxio File Checksum Verifier is donationware, so if you use it and like it, send along a little money to fund future development.