What is the most important scientific idea of all time?
Obviously, the answer to so rich a question is up for grabs, but let me opt for uniformitarianism, the idea that the present is the key to the past and future.
Uniformitarianism assumes that the same laws and processes we see operating in the world today were at work also in the past. If we want to understand the history of the universe, the Earth, or of life, we create our explanations using the world as we find it today. No unique causalities. No miracles. No changing laws of nature.
You run the tape backwards from the present. Or, if you wish, into the future. You follow the tape wherever it leads, even, perhaps, to the big bang itself.
Maybe I shouldn't call this a scientific idea, but rather a philosophical principle. It is not something we can prove, not having direct access to the past or future. But the application of the uniformitarian idea was fundamental to modern geology, evolutionary biology and cosmology. It was the door that opened onto the grand vistas of modern science. The proof of the pudding, as they say, is in the eating.
The idea has a long pedigree, but it is usually credited to James Hutton, the 18th century Scot sometime gentleman farmer and sometime Edinburgh bon vivant. Fiercely resisted at the time, for both scientific and religious reasons, it triumphed -- in Lyell's geology, Darwin's biology, and Hubble's cosmology -- by the sheer grandeur of its explanatory power.
It is not an exaggeration to say that we have yet to encounter reliable evidence of any past event that cannot be explained -- at least in principle-- by natural processes acting in the world today.