Exceptions, are situations where the processor needs to stop executing the current code because of an error. In these cases, the processor typically begins running an exception handling routine to resolve the error, and then returns to the normal program flow. For instance, if the ALU attempts to divide by zero, or if an addition causes overflow, an exception might be triggered. The processor needs to stop operation and fix the error before the program can be resumed.
Some common examples of exceptions are arithmetic overflow or underflow, division by zero, or attempting to access a memory location that does not exist.