A checksum is the electronic "signature" or "fingerprint" of a file. A special program generates the checksum by examining the data in the file. If even one byte in the file changes, the checksum signature will change.
Checksums are often used to verify file downloads. If you download a file, you can see if its checksum matches the checksum posted on the download website. If the two signatures are the same, you can be reasonably sure that your download matches the file offered by the site.
A checksum is not an absolute security solution. If a site is compromised, its checksums may also be compromised. But checksums are a key ingredient in securing data integrity.