axiom is a statement taken to be true without proof, serving as the foundation from which the other claims in a system are derived.
In formal use — logic, mathematics, and the sciences that borrow their method — an axiom is a starting premise chosen for its usefulness rather than established by argument. Euclid's postulates are the standard example: nothing proves them, and everything in classical geometry follows from them. Change an axiom and a different but internally consistent system results, which is how non-Euclidean geometry arrived. In looser use the word names an established rule or a self-evident truth, and in its loosest sense a 📝maxim widely accepted on its intrinsic merit.
The word entered English in the fifteenth century through Latin from the Greek axiōma, "that which is thought worthy," built on axios, "worthy." The etymology encodes the logic: a starting point earns its place by being worth granting, not by being proven.
An axiom differs from a 📝principle, which guides conduct or reasoning rather than grounding a formal system, and from a 📝truism, which is obvious rather than foundational. The distinction that matters most is that a truism is too evident to be worth stating, while an axiom is deliberately assumed so that everything after it can be stated at all.