The bundle of 20th-century institutions through which modern states assume responsibility for providing, subsidizing, or guaranteeing a baseline of income security, health care, education, housing, and protection against the major risks of industrial life (unemployment, sickness, disability, old age). "Welfare state" as a term of art dates to the 1940s — William Temple's use and the Beveridge Report of 1942 — though the institutions it names grew over a century.
Its intellectual ancestors are more various than is sometimes admitted. Thomas Paine's Agrarian Justice (1797) proposed what would now be called a citizen's grant. Bismarck built a pioneering social-insurance system in 1880s Germany to undercut socialist agitation. British "New Liberals" (T.H. Green, L.T. Hobhouse) theorized an expanded role for the state within liberal premises. The Swedish social democrats in the 1930s built the most systematic early welfare state. John Maynard Keynes's macroeconomics gave postwar governments the tools and the confidence to sustain full employment and finance expanded transfers. Beveridge's report crystallized the postwar British model.
Gøsta Esping-Andersen's influential Three Worlds of Welfare Capitalism (1990) distinguished three broad regimes: liberal welfare states (US, UK, means-tested, modest), conservative/corporatist welfare states (Germany, France, stratified, status-preserving), and social-democratic welfare states (the Nordics, universal, generous). Each embeds a different answer to the question of how much of social life should be "decommodified" — freed from direct market dependence.
The welfare state has been contested from the beginning: from the right (it's paternalistic, distortionary, fiscally unsustainable) and from the left (it accommodates rather than challenges capitalism, co-opts working-class politics, and its post-1980s retrenchment under Neoliberalism proved how limited its guarantees were). It remains, for all that, the signature institution of mid-20th-century liberal-democratic modernity.