A Riemann Surface is a one-dimensional complex manifold that allows for the study of complex functions in a more geometric way. It provides a way to visualize multi-valued functions, such as the square root or logarithm, by creating a surface where each point corresponds to a unique value of the function. These surfaces are named after the mathematician Bernhard Riemann, who contributed significantly to complex analysis. Riemann surfaces can be used to understand the behavior of functions, their singularities, and their branch points, making them essential in fields like algebraic geometry and theoretical physics.