An exception is something that doesn't agree with a rule. Exceptions are unusual.
For example, the rule for making plurals in English is "add an s to the word":
one cat — two cats, one dog — four dogs.
But there are some exceptions to this rule, such as one mouse — two mice,
one man — two men.
This case is an exception to the rule.
Anybody who is late for work will be fired. There will be no exceptions.