A K3 surface is a special type of geometric structure in algebraic geometry. It is a smooth, compact, and complex surface that has a trivial canonical bundle, meaning it has no "twisting" in its geometry. K3 surfaces are important because they serve as examples of surfaces that are neither too simple nor too complex, making them useful for studying various mathematical concepts. K3 surfaces can be defined in several ways, including through complex manifolds or as algebraic varieties. They have rich properties, such as having a finite number of holomorphic forms and being connected to string theory in physics. Their study reveals deep connections between geometry, topology, and number theory.