A mathematical function used to check data transmissions for errors. Some synth manufacturers add checksums to long MIDI sysex transmissions (such as patch dumps) that their synths transmit or receive. The checksum function adds one or two bytes to the sysex when it is transmitted. These bytes contain the result of some mathematical function that is calculated from the other data bytes in the sysex string (a number of different functions exist, and manufacturers may use different ones). When the sysex is sent back to the synth, it re-calculates the checksum on the received data and then compares it to the checksum contained in the transmission. If they don't match, a transmission error has occurred.
The MIDI standard contains no specification for when a checksum should be used, or what to do when a sysex with an incorrect checksum is received. Most synths will silently ignore a sysex with an incorrect checksum; a few will indicate the error to the performer.