Basically, diversifying narrows the spread of possible results, raising the center of the returns bell-curve by reducing the likelihood of extreme results at either the high or low end.
It's largely a matter of basic statistics. Bet double-or-nothing on a single coin flip, and those are the only possible results, and your odds of a disaster (losing most or all of the money) are 50%. Bet half of it on each of two coin flips, and your odds of losing are reduced to 25% at the cost of reducing your odds of winning to 25%, with 50% odds that you retain your money and can try the game again. Three coins divides the space further; the extremes are reduced to 12.5% each, with the middle being most likely.
If that was all there was, this would be a zero-sum game and pure gambling. But the stock market is actually positive-sum, since companies are delivering part of their profits to their stockholder owners. This moves the center of the bell curve up a bit from break-even, historically to about +8%. This is why index funds produce a profit with very little active decision; they treat the variation as mostly random (which seems to work statistically) and just try to capture average results of a (hopefully) slightly above-average bucket of stocks and/or bonds.
This approach is boring. It will never double your money overnight. On the other hand, it will never wipe you out overnight. If you have patience and are willing to let compound interest work for you, and trust that most market swings regress to the mean in the long run, it quietly builds your savings while not driving you crazy worrying about it. If all you are looking for is better return than the banks, and you have a reasonable amount of time before you need to pull the funds out, it's one of the more reliably predictable risk/reward trade-off points.
You may want to refine this by biasing the mix of what you're holding. The simplest adjustment is how much you keep in each of several major investment categories. Large cap stocks, small cap stocks, bonds, and real estate (in the form of REITs) each have different baseline risk/return curves, and move in different ways in response to news, so maintaining a selected ratio between these buckets and adding the resulting curves together is one simple way to make fairly predictable adjustments to the width (and centerline) of the total bell curve.
If you think you can do better than this, go for it. But index funds have been outperforming professionally managed funds (after the management fees are accounted for), and unless you are interested in spending a lot of time researching and playing with your money the odds of your doing much better aren't great unless you're willing to risk doing much worse.
For me, boring is good. I want my savings to work for me rather than the other way around, and I don't consider the market at all interesting as a game. Others will feel differently.
