The invisible hand is an imaginary force, invented (arguably 'discovered') by Adam Smith, to explain the way that markets, composed of selfish desires, can have non-selfish consequences.
It is a classic case of "emergence", where a thing of one type leads to a thing of an entirely different type, when viewed at a different scale.
Allegedly, in the absence of market meddling, a truly free market will see that:
The rich...are led by an invisible hand to make nearly the same distribution of the necessaries of life, which would have been made, had the earth been divided into equal portions among all its inhabitants, and thus without intending it, without knowing it, advance the interest of the society
—Adam Smith, The Theory of Moral Sentiments
Economists and libertarians love this invisible hand business, but not nearly as much as the rich love this little theory. They also have all the power and influence, so they can happily publish and distribute this theory in all of their publications.
I've seen it parodied through a quote like this:
The invisible hand is a force which moves all wealth and power to the richest 1%
Though a more rigorous takedown comes from Joseph E. Steglitz:
Whenever there are "externalities"—where the actions of an individual have impacts on others for which they do not pay, or for which they are not compensated—markets will not work well.