Basically a way to reward shareholders. They're more or less equivalent to dividend, but considered more tax efficient, because capital gains tax is lower than tax on dividends.
The holding period required for long-term treatment is more than enough to qualify for the qualified dividend treatment.
In theory, a hypothetical company with a 1$ dividend every year would see it's stock price rise and fall by 1$ through this cycle. A buyback would see a continuous increase in price.
I specifically called out that choice of timing in my second sentence and explained it further in my third.