"Describes" is used here like "inscribed"
Note that there is an $S$ underneath the integral sign as well. This means that its a surface integral. The integral is carried out over a surface, analogous to how a line integral is carried out over a path.
$\rm dS$ will be a small area element. In most surface integrals, you can write it as a product of two differentials. For example, on a plane (parallel to $xy$ plane), $\rm dS=\rm dx \rm dy$. For a sphere, $\rm dS=r\rm d\theta \times r\sin\theta\rm d\varphi $.
Question: Are you trying to learn optics via Wikipedia(looking at your previous questions). Wikiepdia is a bad place to learn stuff--its a reference--which means that it assumes you know everything and want to know more :/. I suggest getting a textbook if you are Wikipedia-studying. There also are free online lecture videos and material, like those from MIT or Khan Academy.