An exception (more often condition) refers to facilities in some programming languages and operating systems to indicate the occurrence of some sort of error or un-expected event - e.g. 'divide by zero' or 'unexpected end-of-file'.
The term 'exception' is also often used for hardware-detected issues (e.g. in the Motorola 68000 Family), where a trap is the usual result; the term 'condition' is usually more general, and covers software-detected and generated issues. Software is said to raise or signal a condition.
When such an event happens, program execution is diverted to an condition handler for that specific condition, which is expected to deal with that condition.