We don't always know the exact solution of Laplace's equation, but we do know that every solution has the property that the value of the potential at some point can be obtained from the average of the nearest neighbors. The relaxation method is applied to a matrix of boundary conditions, where we update the matrix by replacing each element with the average of its nearest neighbors. After a given number of iterations, the matrix converges and by the uniqueness of the potential theorem, this is the solution to Laplace's equation in that interior region with the specified boundary conditions.