Kernel
Von Neumann is the figure who, between 1925 and 1955, contributed first-rate work to seven distinct disciplines: pure mathematics (functional analysis, operator theory, set theory), quantum mechanics (the Hilbert-space formulation), game theory, computer architecture (the stored-program design that bears his name), nuclear weapons, weather modeling, and the theory of self-replicating automata. He is the supplier of the operational architecture of modern computing.
Contribution
Stored-program architecture (the 1945 EDVAC draft, the basis of essentially every general-purpose computer since). Operator-theoretic foundation of quantum mechanics. The 1944 Theory of Games with Morgenstern. The Manhattan Project implosion-lens design. Cellular automata. The mean-value theorem in functional analysis that bears his name.
Lineage
Budapest's Lutheran Gymnasium (Eugene Wigner and Edward Teller as classmates), Berlin and Göttingen for his mathematics training, Princeton's Institute for Advanced Study from 1933. The Manhattan Project mathematics group reports through him. Most of the computing tradition runs through his 1945 architecture.
Civilization-scale significance
If there is one figure whose intellectual output explains the postwar U.S. technical supremacy, it is von Neumann. Modern computing, the bomb, and game theory are his three foundational contributions; any one would be sufficient.