At first the title of the story seems pretty straightforward. It seems mostly descriptive: this is a story about something that happens at Owl Creek Bridge. All true enough. What we find interesting is Bierce's word choice. He could have gone with any word in the dictionary, but he chose "occurrence." We're pretty sure that anyone being hanged would think that the word "occurrence" was a bit too casual a description. But maybe that's the point? The word "occurrence" seems so laid back, so blasé, that it almost sounds like he's writing it off as a no-big-deal, everyday kind of a situation. Is this a cynical commentary on military violence? Sure sounds very Ambrose Bierce to us.
An occurrence, according to the Oxford English Dictionary, is an event or a happening. Simple enough, right? Not so fast. The "currence" part comes from the Latin word currere, meaning "to run."This is very much related to the word "current," as in running water. We can't be sure whether or not Bierce was thinking about this when he wrote his story, or even if he knew this little etymological nugget to begin with. But, the story begins with a man staring down at a creek (a creek with a current!), and so we're going to go ahead and (over)analyze.
If we really wanted to go off the deep end, we could say that present in both the title and in the creek below the bridge, a current runs through the story. The current could represent life, or time, or fate, or freedom. But maybe that's digging a bit too deep into the word "occurrence" – you decide.