What does this line in Lang's "Algebra" mean? Lang's "Algebra" says the following:

Let $S$ be a set. A mapping $S\times S\to S$ is sometimes called a law of composition (of $S$ into itself).

I always thought $S\times S\to S$ implied a binary operation on two elements of $S$, and $S$ being closed on that binary operation. 
I also thought the word "composition" belonged to the world of mappings.
I don't see how a binary operation can be called a mapping.   
EDIT: I must confess I have come across such a usage of the term "composition" before, but could never quite get the motivation behind it. Really hoping for an elaborate answer to shed light on this issue; something that I am sure confuses other autodidacts out there too. 

The phrase “law of composition” is a direct translation from the French loi de composition (usually also interne is added). See Bourbaki, Éléments de Mathématique.
It's just a name and has nothing to do, in general, with function composition. Indeed, Lang says that sometimes a map $S\times S\to S$ is called a law of composition, probably aware of the fact that this locution is not very used in English speaking countries. It used to be frequent also in Italian text, under the influence of Bourbakism.
A binary operation is just a map (or mapping, if you prefer): to any (ordered) pair of elements in a set $S$ it associates an element of $S$. So it's best treated as a map (mapping, function, application, representation are also used), without introducing new concepts that aren't useful.
