W. K. Hastings published this paper in Biometrika in 1970, taking the sampling idea that Metropolis and colleagues had introduced in 1953 for physics and recasting it as a general statistical tool. The 1953 method assumed a symmetric way of proposing new candidate states; Hastings showed how to relax that assumption, allowing almost any proposal distribution as long as the acceptance probability is corrected accordingly.
The result, now called the Metropolis-Hastings algorithm, gives a recipe for drawing samples from essentially any probability distribution you can evaluate up to a constant. You repeatedly propose a move, then accept it with a probability that depends on the ratio of the target densities and the proposal densities. The chain of accepted states eventually behaves as if drawn from the target distribution, even when that distribution is high-dimensional and has no tractable formula.
The paper also works through practical concerns that still occupy practitioners, including how to choose proposals and how to assess the error in the resulting Monte Carlo estimates, and it touches on what would later be recognized as componentwise updating.
For a business or general reader, the importance is that this single algorithm made Bayesian methods computable in practice. Decades later it underpins much of applied statistics, from clinical trial analysis to the probabilistic models behind many machine learning systems, because it lets analysts answer questions about models that could otherwise only be written down, never actually solved.