In neoclassical economic theory, the "Invisible Hand" refers to the mathematical result that, in models that assume rational economic agents, the behavior of those agents, in pursuing self interest, is "Pareto Optimal".

Pareto Optimality means that there is no way to reallocate resources to make wo agent better off without making another agent worse off.

Applied to actual economic systems, the idea is that, to the extent that the actual economic system is Pareto Optimal, that optimality is a beneficial order that emerges spontaneously from the pursuit of self interest by individuals.

The policy implications are (1) that there is no need for government to attempt to coercively impose such economic order, and (2) that attempts to do so are likely to make things worse, not better.

[See] [Invisible Hand] "In contrast to Smith's own usage, the "invisible hand" today is often seen as being specifically about the benefits of voluntary transactions in a free market, and is treated as a generalizable rule."