I'm sure you've heard someone say something like this:
We had an incidence last week where someone used a word incorrectly
Although it can be confusing, the word incidence doesn't work in that sentence. Incidence means the rate of occurrence, and is an uncountable noun (like rice or information). You can often substitute the word frequency—if that wouldn't work in a sentence then you know incidence won't work either.
Sometimes people use incidence when they are really reaching for the word incident but trip over the word instance along the way. In fact, sometimes people accidentally use instance incorrectly:
We had an instance last week where someone used a word incorrectly
An instance is a case or occurrence of something. Programmers will recognize this usage immediately: an instance is an object created from the definition of a class. Most of the time, though, you will see the word of after the word instance:
Last week there was an instance of incorrect usage.
You can often substitute the word example for the word instance to see if the sentence works. Most of the time, the word instance can use a little explanation in the same way as the word example.
An incident is also a kind of occurrence, of course, but doesn't need to be explained in the same way:
We had an incident last week.
It's often the word incident that people are looking for when they settle on incidence or instance. To see if it's really incident that you want, try substituting accident.
For more on incidents and accidents, hints and allegations, see "You Can Call Me Al" by Paul Simon.
Yes! ("Don't want to end up a cartoon
In a cartoon graveyard...")