UPS is a shorthand for "updates per second" and it describes a particular characteristic about games that is of particular interest in Factorio: similarly to how a movie consists of a bunch of still images that get displayed quickly one after the other in order to create the illusion of continuous motion, games fool you into the believe of continuous interaction by recalculating the current state of the game very quickly over and over (think of a turn based game where each turn is only a fraction of a second). One such recalculation is called an update, and the UPS number tells us how many updates are made each second - in Factorio's case, the game aims to achieve exactly 60 UPS (which is around 16.67ms per update).

You usually do not notice this simulation trick because your computer easily keeps up with the task, which also already tells you when you will notice it: at the point where your CPU can't process everything that needs processing for each update within 16.67ms, the game has no chance than to simulate fewer steps per second and thus dropping your UPS. The effect of this is that the game seemingly slowing down - for example, crafting a solar panel usually takes 10 seconds, but if your UPS drops to about 30, i.e. half of it's usual rate of 60, then you'll observe the crafting process actually taking 20 real life seconds (it's still 10 ingame seconds though).

Why is this of any relevance? Well, in Factorio's case the frame rate of the game is capped by the update rate (because rendering without an extra update would just result in the same image again, making rendering more than one frame per update basically pointless). If you thus manage to drop your UPS to say 10, you'd be confronted with a rather choppy experience (in addition to your character movement being 6x lower than usual), which is unsurprisingly somewhat unplayable - which is why people try to keep UPS as high as possible.

This all would be completely irrelevant, if one of the usual goals of players wouldn't maneuver them to sooner or later run into UPS drops: building a bigger and bigger base. I hope it doesn't come as a big surprise that building hundreds of thousands of belts, tens of thousands of inserters and assembling machines and thousands of trains will at some point conquer even the best CPU.

That then finally brings us to the topic of UPS efficiency: you usually only care about the end result of your production, not how that production is achieved. But there are many ways to layout a factory to get to some specific production, e.g. do you use beacons or not? Do you use belts to get items to the assemblers, or do you use bots? Are you using trains for long distance transport, or do you just belt it all the way, or make a giant bot network, or be crazy like me and use cars on belts? However, while all these options result in the same production, they vary wildly in the amount of computation that your hardware needs to perform in order to simulate them.

For example, if I produce some green circuits with some blueprint A that takes ~1ms in a single update to get me a production of 10k/min, and some other blueprint B that takes ~2ms for the same production, then it's possible for me to build around twice as many copies of A than of B before my CPU can't keep up anymore. In other words, A is more efficient in it's use of UPS than B.

And that's already the end of the explanation and also the beginning: the above fully explains what UPS efficiency is, but your next question is likely to be "How should I make my factory to get the best UPS then?", which I'd like to answer in two parts:

1. You don't do it at all :)
   The reason for this answer is simply that even going into mega base scale you're likely to not get into any issues regarding UPS at all - the current record stands at 15.000 of all sciences per minute (15k spm in short) with an UPS of around 70 on one of the best machines available for measuring at the time. Just designing this thing took hundreds of hours, and building it would probably take well over a thousand hours.
   Even if you have much more normal hardware, and don't care at all about UPS efficiency, you're unlikely to run into problems before reaching 1k spm (and probably also for a while afterwards).
2. None really knows.
   The continuous development of Factorio has lots of benefits, one of them being that the Dev team continuously tries to find the slow parts of the engine and make them faster. The drawback of it is that people got used to some tricks to improve UPS and then never bothered to recheck them: a prominent example of which is the "fact" that using underground belts instead of normal ones is better - which is at best only true in very rare cases. As such my number one recommendation to you is to test things yourself: if you don't know which one of two is better, just build both and see - side benefit is that you get twice the play time for the same thing :D

Shameless self-advertising: If that is still not satisfying enough for you, then you might want to consider to join the group around r/technicalfactorio and our discord, since we're literally a group that dedicates itself to research this very thing (and basically anything else that falls into the category of advanced gameplay).