Starting with the curl of a vector field, we can interpret the resulting vector field as the extent to which the initial vector field curls around a particular point. Say we now take a service integral of the curl of a vector field. We are basically calculating the total amount of curl in this surface. And you can imagine that this curl can add up constructively or destructively. So we might as well calculate the effective amount of curl by going along the boundary of the surface. This is called Stokes-theorem. It tells you that the surface integral of the curl of a vector field is equal to the line integral of the vector field along the boundary. Since the right-hand side depends only on the path and not on the particular surface that is chosen, the left-hand side doesn't depend on the shape of the surface. And since for any closed surface, the path is essentially zero, so the closed surface integral of the curl should also be zero. Stokes-theorem plays an important role in several Maxwell equations.