From Latin alligare (to bind to), through French aliance — an alliance is literally a binding together
A formal agreement or union between nations, groups, or individuals for mutual benefit or protection
From Old French 'aliance' meaning union, connection, or marriage, from 'alier' (to ally, to unite), from Latin 'alligare' meaning to bind to, from 'ad-' (to) and 'ligare' (to bind). The core image is of binding one thing to another. Latin 'ligare' produced a vast family of English words related to binding, obligation, and connection. The political sense of a formal pact between states
The same Latin root ligare (to bind) that gives us alliance also gives us religion (possibly from re-ligare, to bind back or to bind tightly), obligation (a binding duty), ligament (tissue that binds bones together), and league (a binding agreement). The idea of being bound together runs through English words for everything from anatomy to theology.