Alliance comes from binding. The word traces through Old French aliance (a union or bond) from the verb alier (to unite), descended from Latin alligare, meaning to bind to. The Latin compound joins ad- (to) with ligare (to tie or bind). At its root, forming an alliance means tying yourself to another party.
Latin ligare produced one of the largest word families in English. Ligament (tissue binding bones), ligature (a binding thread or tie), oblige (to bind by duty), religion (possibly from re-ligare, to rebind or reconnect), rely (to bind oneself back to), and league (a binding compact) all descend from the same root. Ally itself is a direct descendant, as are liable, liaison, and lien. The concept of binding permeates English vocabulary for duty, connection, and commitment.
In medieval usage, alliance meant primarily a bond through marriage. Royal and noble families formed alliances by marrying their children to each other, creating political ties through personal bonds. This matrimonial sense persisted for centuries alongside the purely political meaning. The French word alliance still refers to a wedding ring.
The political sense narrowed over time to mean specifically a formal pact between sovereign states, usually for military cooperation or mutual defense. The Triple Alliance and Triple Entente of pre-World War I Europe, NATO after 1949, and the various alliances of the Cold War era all use the word in this precise diplomatic sense.
Business adopted alliance in the late 20th century for cooperative arrangements between companies — strategic alliances, airline alliances, technology alliances. This commercial usage preserves the core meaning of binding together for mutual advantage while stripping away the military and matrimonial overtones that dominated the word for most of its history.