A checksum is a hashing algorithm where SHA is an acronym for Secure Hash Algorithm.
These are used to generate a unique hash result for any file. The checksum file itself is a text document that contains the hash generated. Copies of the file can be checked to make sure they are exactly the same - if the file is changed in any way, either intentionally or by corruption, the generated code will be different.
Manjaro uses SHA-256 or SHA-512 to generate the checksum.
If the code genrated from the disk image matches what is contained in the the checksum file, the disk image is considered safe. If they do not match the disk image - the ISO - has been altered - possibly during download.