The advice about MTBF not being useful for prediction is all true. But it's even less useful than people who are aware that it isn't useful tend to think.
Life Expectancy
Different kinds of failures at different stages of life
The graph of the "bathtub curve" in wrecclesham's answer is a conceptual diagram. In reality, the two ends can be proportioned a little different. For example, if a manufacturer uses good quality parts and good manufacturing quality control, the infant mortality can be very low.
Failures at different stages in a product's life are largely for different kinds of reasons. During the infant mortality period, products fail because of defective parts or manufacturing defects. If they don't fail early, they go through a period of "attrition". Some small percentage of units fail each year for random reasons. By end of life, parts are wearing out and failures happen because that's how much use the components were built for.
Big differences in build quality can affect failures at all stages to some degree. A very cheaply made product may use cheap parts, poor manufacturing precision, and have generally little attention to quality control. A high-end product would likely be the opposite on all counts.
Products in the same class may not have much difference in build quality. So, for example, the manufacturer could receive a batch of a component part with the normal life expectancy but wider tolerances. It might have a higher percentage of infant mortalities, but if it doesn't fail for that reason, will have the same service life.
Life expectancy of old parts
Life expectancy can actually work in the reverse of what you think. The life expectancy of an average unit includes infant mortality failures and random attrition failures. An old device hasn't failed from either of those kinds of causes. So a pool of just old devices will have a longer average total life than a pool of all new devices.
The longer a device lasts, the more likely it is that it's lasted that long because of its quality. It's one of the lucky few units that got the most perfect components, was manufactured with the greatest precision, and got the best handling and care. Given that you have an old part that is still working, it isn't expected to fail momentarily because that's how long the average unit lasts. Your old part has a longer life expectancy than the average unit (although that still tells you nothing about how much longer your specific unit will last).
MTBF
What it is
The term "MTBF" is used in several ways. "Mean Time Between Failures" is used as a measure of expected system uptime or availability for repairable systems. "Mean Time Before Failure" is applied to devices that may or may not be repairable, but it is often associated with end-of-life events. That's the applicable meaning here.
The name of the measure, "Mean Time Before Failure", is very misleading. It usually isn't really that. You would measure that definition by running a quantity of the units until they failed and then take an average of those times. For items with an expected lifespan of many years, that would be impractical; the products would never make it into the marketplace because they would forever be in testing.
The number is developed another way. When it isn't simply extrapolated from the bogus number for a similar model, the method often used to measure "MTBF" is to test a large number of units for a relatively short time. They divide the total test hours (test duration x number of test units) by the number of failures during that time (and they typically don't stop the clock on a per-unit basis when it fails).
What it really measures
The failures that happen during this timeframe are infant mortalities and random failures during the early part of their lives. They never get to the end-of-life failures, which is what you want to know. Only a small percentage of units fail early in their life. You can't extrapolate or derive time to end-of-life from those statistics, they really tell you nothing about life expectancy. At best, they're a crude relative measure to compare one item to another.
Looking at the events MTBF is based on, the attrition failures are random events that happen with any product, regardless of quality. A product of substantially higher quality will last longer because the parts take longer to wear out, but the random failures before that may not be much different.
So differences in MTBF tend to mostly reflect differences in infant mortality, not end-of-life. As described earlier, that could potentially reflect a difference in build quality, which might translate to some difference in life expectancy. But it could also be a case of high quality devices where the manufacturer received a bad batch of one component. If your device isn't one with the bad component, it could have a much longer life expectancy than the average unit.
Does MTBF have any practical value?
If you have a choice between two products, where MTBF was estimated the same way for both (say two different models from the same manufacturer), and one product has a substantially better MTBF, that might be a sign of generally better quality, and you might expect it to last some amount longer. All else being equal, the safer bet would be to go with the one with the better MTBF.
If the MTBF numbers are close, small differences are just statistical noise; it tells you nothing at all.
