What does the quote, "Power serves to create power. Powerlessness serves to reinforce powerlessness" mean? Does it mean that those with power remain powerful, and those without power aren't able to rise above powerlessness? Can you please elaborate?
It's obviously impossible to know what was meant by whoever said it as you didn't provide any context.
But the general idea, in a politics and game-theoretical sense, is that when someone has power (to do things), they can - and frequently do - use that power to effect changes and outcomes which serve to enhance their power.
Examples from real life would include:
"Incumbent advantage" in politics.
The person already holding a political position, by virtue of holding it, has the power to do things that help them get re-elected (or elected to higher position) - they can pass popular/populist laws; they can make speaches; they can get financial contributions from people who hope to get (or already got) contracts or fevorable decisions from the government.
If you have financial means, it's easier to grow your wealth (e.g. you can have investment profits in general. Or, if you have enough money for a margin account, you can short stocks. Or you can wait until specific market segment cycles down and invest in that buying low).
If you have wealth, it's easier to obtain loans with low interest rate - because you're less of a credit risk. Which is of course how lending should work, but it still benefits those who need the lending the least, most.
Vice versa, if you don't have power, you have no way to sway things to help you gain power - or to stop people who have power from swaying things so you lose even more, in zero-sum situations.
Evolution in general
Let's say you have 2 organisms, with one more fit than another. Let's say the first one is stronger. If they are, they can take the food away from the weaker one (in many cases, it's a zero sum game as there's not enough food for everyone to get enough). They get more food which makes them even MORE fit (being well fed) and the weaker one even LESS fit (being undernourished). There are game theoretical models and equasions describing the phenomena, but details would be more on topic on Biology.SE
As an aside, please note that this sometimes gets incorrectly universally misinterpreted as always being true, even though very frequently, the "zero-sum" requirement isn't met. For example "the rich are getting richer and poor are getting poorer" is a nice soundbite, up until you realize that in most Western countries, the quality of life of the poor is significantly improved compared to both the recent; and even more so the not-so-recent past; due to the fact that quality of life isn't usually a zero-sum game in Western economy.