ALIEN: Explain to me this "election".
HUMAN: Well, we humans are social primates. Social animals commonly exist in small groups with a dominance hierarchy. They'll have some procedure for establishing social status, and this can be used as a proxy for the outcome of physical conflict. This way, every wolf in the pack doesn't have to be fighting every other wolf for food or mate selection or whatever. They'll only come into occasional conflict with other wolves that are marginally stronger or weaker than themselves.
ALIEN: With you so far...
HUMAN: Some social animals, particularly higher primates, are sophisticated enough to form coalitions. The largest chimp in a troop might be able to fend off any individual rival, but can't fend off the two largest rivals working together. Chimpanzees, bonobos and gorillas all exhibit coalition-forming behaviour. The largest chimp, to secure his position, can concede some food or mate selection options to the second-largest chimp. Alternatively, the second-largest chimp can make the same offer to the third-largest chimp. This is more sophisticated than it might seem to modern humans. "Make me leader and I will give you stuff" is a notion that's available to chimps.
HUMAN: So humans, as well as being primates, are also capable of advanced long-term planning and shaping our surroundings. We can overcome environmental limitations like food scarcity and harsh climate to coexist in bigger and bigger groups and carry out social projects on a longer and longer time-scale. For a troop of chimpanzees, the most sophisticated social project might be "let's go and live in that clearing over there". For humans, the most sophisticated social project might be "let's go to the moon". Just as the chimps might fight about the clearing, the humans will fight about the moon.
ALIEN: So the biggest human that wants to go to the moon forms a coalition with other humans who want to go to the moon, and promises food and mates to other humans who are indifferent to going to the moon, creating a group with greater social status than the non-moon goers, so the non-moon-people will defer to the moon-people rather than entering into conflict?
HUMAN: Well, large social projects such as going to the moon or not murdering each other are quite fragile. In smaller groups humans still behave a lot like chimpanzees, but in larger groups we need special social projects to let everyone work together. How these social projects are run is something people would fight about a lot. If the biggest human with the most supporters could just turn up and change this social project to their whim, this would be bad. So we have more elaborate procedures for deciding who has control over those social projects.
ALIEN: Okay. I was worried for a minute that humans organised their society by having people with a lot of social status say "make me leader and I will give you stuff", those people forming the biggest, strongest group, and having everyone else defer to them. It's good to know you've got a better system than that.
HUMAN: Well, uh...
ALIEN: Oh, sweet blue buggery...
HUMAN: Look, we might have six thousand years of civilisation, but we're still basically primates. "Make me leader and I will give you stuff" is still the rough template we go by, but we've learned a few things about how this should work. It's quite important that a clear procedure exists for selecting the next leader, for example. If leadership is contested, you get power struggles and instability. It's also important that the leadership has some sort of "legitimacy", in the sense of people accepting that the leadership is there through a collectively-sanctioned process. Also the leadership needs to persist long enough to accomplish things, but not so long that bad leadership can't be removed without blood running through the streets. It's also generally the case that the more people the would-be leader has to promise to give stuff to, the less stuff that leader can keep for themselves.
ALIEN: So the election..?
HUMAN: ...is a well-defined procedure where all humans in a large political community (who meet some eligibility criteria) register their preference for which coalition of high-status humans are given short-term control over a selection of large and important social projects.
ALIEN: And how is it working out for you?
HUMAN: I'll admit it could be going a little better, but given it started out as chimps ganging up to kill each other, it's an absolute miracle.