The PSU supplies power to your components. Your components for the most part have power regulation circuitry to control voltage in response to varying loads. Some will actually intentionally change voltage (i.e. CPU, GFX Card, MoBo fan control). The other aspect is maintaining a stable voltage .... if the CPU wants 1.275 volts, your MoBo must work to maintain a constant 1.275 as if it's jumping all around, the MoBo has to work harder to maintain stability. If your PSU has voltage swing wildly, especially at hi loads, then that job gets much harder. Voltage instability is an enemy of high overclocks.
Another one is noise / ripple..... dirty power is another enemy of high overclocks..... voltage instability and dirty power put more 'wear and tear" on your components. The other aspect of course is that whatever power is not converted from the wall socket and doesn't produce power in the PC is wasted as heat. The heat adds to the heat load in the case.
Finally, quality components last longer and do their jobs better. Capacitors age over time which lowers the available power output. If you have ever used a quality PSU calculator you will see that they have an entry for an allowance for capacitor aging..... on a good PSU, 10% is a reasonable number.... on the other end of the spectrum, it might be 35%. Protection circuitry also improves with higher quality components meaning that is something goes awry, that higher end PSU with better circuitry will do a better job protecting your components than the cheaper one.....they good ones also don't go on fire
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While I did my best to provide a layman's description, you can do a web search on the topic and come up with many detailed technical articles on the subject.
Lastly, buying by brand name or even model line is a fool's errand. Just about every manufacturer makes a wide variety of PSUs and since they are in business to make money, they usually don't limit themselves to a single price range or market niche ..... So just because the "SuperPSU Company" makes a $180 SD 850 model, does in now way suggest that the $79 model is worth getting. Even the OEM is not a clear indicator of quality. You will oft see it posted that Corsair is a good PSU cause they are made by Seasonic ..... and while Seasonic does make some fine PSUs (X series if my 1st choice), the best PSUs (HX series) were made by Channelwell .... and yes, CW made both the great HX850 and the crappy HX1050.
You can buy two PSUs from the same company and one could be great and one could be one you wouldn't want to put in a performance oriented PC .... i.e. Corsair HX750 = Excellent Choice / Corsair CX750 = Poor Choice
You can but two PSUs within the same line and one could be great and one could be one you wouldn';t wanna own .... i.e. Corsair HX850 = Excellent Choice / HX 1050
HX1050 -
http://www.jonnyguru.com/modules.php?name=NDReviews&op=Story5&reid=245
Performance = 8.5
Build Quality = 7
HX850 -
http://www.jonnyguru.com/modules.php?name=NDReviews&op=Story5&reid=299
Performance = 10.0
Build Quality = 9.5