Axioms are fundamental statements or principles that are accepted as true without proof. They serve as the foundational building blocks for a system of logic or mathematics. For example, in geometry, the statement "through any two points, there is exactly one straight line" is an axiom that helps define the relationships between points and lines. In mathematics, axioms are used to derive theorems and other truths. Different branches of mathematics may have their own sets of axioms, such as Euclidean geometry or set theory. These axioms provide a consistent framework for reasoning and problem-solving within their respective fields.