There is burn-in and then there is burn-in. In semiconductor manufacturing terminology "burn-in" is a stage of the production flow after packaging in which the CPU is placed in an elevated temperature environment and is stressed at atypical operating conditions. The end goal of this is to dramatically reduce the statistical probability of "infant mortality" failures of product on the street. "Infant mortality" is a characteristic of any form of complex manufacturing in that if you were to plot device failures in the y-axis and time in the x-axis, the graph should look like a "U". As the device is used, initially quite a few fail but as time goes on this number drops off (you are in the bottom of the "U" in the graph). As the designed life of the product is reached and exceeded, the failure count rises back up again. Burn-in is designed to catch the initial failures before the product is shipped to customers and to put the product solidly in the bottom section of the "U" graph in which few failures occur. During this process there is a noticeable and measurable circuitry slow-down on the chip that is an unfortunate by-product of the process of running at the burn-in operating point. You put a fast chip into the burn-in ovens and it will always come out of the ovens slower than when it went in - but the ones that were likely to fail early on are dead and not shipped to customers.
There are two mechanisms that cause the circuitry in CMOS - particularly modern sub-micron CMOS - to slow down when undergoing the burn-in process: PMOS bias-temperature instability (PMOS BTI) and NMOS hot-electron gate-impact ionization (known as "NMOS hot-e"). Both of these effects are complex quantum-electrical effects that result in circuitry slowing down over time. You should be able to type either of these two terms into Google to read more about what is actually happening. The end-result is, as mentioned, that the chips will start to fail at a lower frequency than they did before going into burn-in due to the transistor current drive strength being reduced.
There is another use for the term "burn-in" with regard to chips that is used by system builders and that is as a test for reliability and to reduce customer returns due to component failure. This usually consists of putting the system together, plugging it in and running computational software on the system for a period of 24-48 hours. At the larger OEM companies, this is often done at a higher than typical operating temperature.
Some time ago someone on the internet wrote a very factual sounding article on the benefits of running a CPU at a higher than typical voltage for a day or two to improve it's "overclockability". This author wrote some scientific sounding verbiage about how NMOS hot-e actually improves the drive strength of PMOS devices as a supposed explanation for why this method works. Reading this particular article and, even worse, seeing people commenting that this was a wonderful article that everyone should follow was the reason why I started posting on AnandTech way back when. The author was wrong on several key points - primarily that NMOS hot-e can occur in electron-minority (hole majority) carrier devices that are biased such as to repel electrons - and I contacted the author with a wide assortment of technical journals showing that he was wrong. He was not particularly open to the fact that he might be mistaken and never remove the article from the website that I'm aware of. Suffice to say, however, that he did not understand basic semiconductor electronics and was wrong.
There is no practical physical method that could cause a CPU to speed up after being run at an elevated voltage for an extended period of time. There may be some effect that people are seeing at the system level, but I'm not aware of what it could be. Several years ago when this issue was at it's height on the Internet, I walked around and talked to quite a few senior engineers at Intel asking if they had heard of this and what they thought be occurring. All I got were strange looks followed by reiterations of the same facts as to why this couldn't work that I had already figured out by myself. Finally, I was motivated enough to ask for and receive the burn-in reports for frequency degradation for products that I was working on at the time. I looked at approximately 25,000 200MHz Pentium CPU's, and approximately 18,000 Pentium II (Deschutes) CPU's and found that, with practically no exceptions at all, they all got slower after coming out of burn-in by a substantial percentage.
To me there is no doubt in my mind that suggesting that users overvolt their CPU's to "burn them in" is a bad thing. I'd liken it to an electrical form of homeopathy - except that ingesting water when you are sick is not going to harm you and overvolting a CPU for prolonged periods of time definitely does harm the chip. People can do what they want with their machines that they have bought - as long as the aware that what they are doing is not helping and is probably harming their systems. I have seen people - even people who know computers well - saying that they have seen their systems run faster after "burning it in" but whatever effect they may or may not be seeing, it's not caused by the CPU running faster.
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