1. A frequent consequence of data arriving faster than it can be consumed, especially in serial line communications. For example, at 9600 baud there is almost exactly one character per millisecond, so if a silo can hold only two characters and the machine takes longer than 2 milliseconds to get to service the interrupt, at least one character will be lost.
2. Also applied to non-serial-I/O communications. "I forgot to pay my electric bill due to mail overrun." "Sorry, I got four phone calls in 3 minutes last night and lost your message to overrun." When thrashing at tasks, the next person to make a request might be told "Overrun!" Compare firehose syndrome.
3. More loosely, may refer to a buffer overflow not necessarily related to processing time (as in overrun screw).