It works like this: Each of the women proposes to her first-choice man, and he rejects or accepts. Women still without a partner approach their second-choice man (the women can propose to men who have already accepted an offer, and the men can choose to reject an initial proposal if a better offer comes along). This continues until there are no women left who want to propose to a man.
I found this article interesting because a friend of mine is experiencing this process, but also because I think it would be a simpler way to job search. The FiveThirtyEight twitter account seemed to think it could be applied to college applications too. The ironic thing is that I do not believe that any online dating website has actually implemented this algorithm.