The procedure to generate a checksum is called a checksum function or algorithm. Typically, a good checksum function would output significantly different values even for small changes made to the input. Checksum functions are typically related to cryptographic hash functions (CHF), randomization functions, fingerprints and hash functions. Check digits and parity bits are special cases of checksums.
Typically a checksum is generated before sending the data over the wire, and then generated again with the received data. If both hash values match, its very unlikely that the data was altered mid-transit. If they don't match, the data was probably corrupted mid-transit. In that case, the client may re-request the data.