Time-sharing
The idea of letting many users share one computer at once — and thereby the invention of sitting in front of a computer.
Before time-sharing you submitted a job and collected the printout the next day. CTSS at MIT in 1961 showed that a machine can switch between users fast enough that each experiences having it to themselves. Since people think slowly and type more slowly still, the processor is idle most of the time anyway, and that idleness is exactly the space the system exploits.
The consequences ran well beyond the technology. Interactive debugging, text editors, mail between users on the same machine and the whole culture that grew up around terminal rooms all presupposed time-sharing. Commercially it produced the service bureaus, which sold computer time by the hour to companies without a machine of their own — a business model described in much the same terms as the cloud is today.