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. 

Associativity is often considered one of the most fundamental axioms in abstract algebra for a binary operation $S \times S \to S$, and it is well known that a set of functions under the binary operation of composition will automatically satisfy associativity.
Conversely, for a fixed $x \in S$, if we denote the function $t \mapsto x \cdot t$ by $L_x: S \to S$, then associativity can be restated as $L_{xy} = L_x \circ L_y$. Thus we see that the axiom of associativity is precisely the statement that, up to renaming, the binary operation is given by composition of functions on some set. So in the context of an associative binary operation, the term "law of composition" really does make sense.
