A holomorphic structure refers to a mathematical framework in complex geometry where a manifold is equipped with a compatible system of complex coordinates. This allows for the definition of holomorphic functions, which are functions that are complex differentiable in a neighborhood of every point in their domain. Holomorphic structures are essential in understanding complex manifolds and their properties. In the context of complex analysis, holomorphic structures enable the study of various geometric and topological features of manifolds. They play a crucial role in areas such as string theory and algebraic geometry, where the behavior of complex variables is fundamental to the underlying theories and applications.