Chekhov's gun is a literary principle named after the Russian playwright Anton Chekhov. The principle states that every element in a story must be necessary. He made this point in his letters and writings: if there is a gun introduced in the first act of a play, it must be used by the end of the play. Otherwise, it shouldn't have been introduced in the first place.
Chekhov's gun is often used as a metaphor for any element in a story, whether it's a character, object, or plot point. If an element is introduced, the audience expects it to have significance and contribute to the story in some way. If it doesn't, it can create confusion or disappointment for the audience.
Job seekers often agonize over the content of a resume, including formatting, punctuation, and whether to use bullets or not. (side note: as always my recommendation for all things resume related is Guide to Rethinking Resumes by Richard Bolles). One of the biggest concerns is how (or whether) one should list work experience that is not relevant to the position application. The presumption is that on the one hand employers like to see some continuity of employment, and that gaps are bad. On the other hand, if your career took a side tour into professional basket weaving, it may be superfluous and may only serve as a distraction. So--should you include it or not?
If you adhere to the principle of Chekhov's gun, then just as every element in a story must be necessary, every piece of information on a resume should be relevant and contribute to the overall narrative of your qualifications for the job.
Ironically, in act two of The Cherry Orchard, one of Chekhov's most famous plays, a character appears on stage cleaning a rifle. Another character displays a pistol while musing on the subject of suicide. Neither object is referred to again, and they seem to serve no other purpose in the play. All that is to say that Chekhov didn't follow his own advice.
The traditional approach is to list your work history in chronological order. But this is based on the idea of the linear career, which is a bit unusual in this industry. As I mentioned in a previous post, if you're a Phoenix type, your road to success may have a variety of twists and turns that got you to where you are. Everyone is entitled to a tangent or two.
Additionally, by now it must be obvious that you really have two resumes; the first is the one you submit, and the second is your "Google" resume, or online presence. Any employer worth their salt will immediately look for your online profile on Facebook and LinkedIn and every other online platform as well if they're interested in you and looking for a good fit for their organization. If you didn't know, now you know.
So we dispense with Chekhov's gun and the notion that there's no such thing as irrelevant information, only information that gives context to who you are. Remember that the principle goal for the employer is to find a candidate that will fit well with the organization. Experience is often secondary. It's possible that your potential boss is into basket weaving.
A more contemporary approach is to list the relevant experience first, and to list "other experience" second. Any employer looking for gaps of employment could take a little time to figure out the sequence of things. In the meantime, they can focus on what's essential. Cleaning the gun may not be essential to the story of your career, but finding a way to convey what is essential while telling the story of your career will ensure that you don't shoot yourself in the foot.