what is the meaning of the notation $f: A\times B \rightarrow C$

I'm reading the 4th paragraph on page 8, under section 1.2 Fields, in the following book https://drive.google.com/file/d/1KQ7dbLXI4x39VwZovTL0DKRsZwt_i3Vt/edit "linear algebra done openly".

the summary is:

a function $f$ is a relationship between sets, say $A$ and $B$...we denote this function relation as $f: A \rightarrow B$... $A\times B$ denotes the set of ordered pairs of elements from $A$ and $B$... An operation is a function of the form $f: A \times B \rightarrow C$. One should think of an operation as a process of bringing two objects together and creating a third operation.

what does:

"An operation is a function of the form $f: A \times B \rightarrow C$. One should think of an operation as a process of bringing two objects together and creating a third operation." exactly mean? what would a good example look like?

An "operation" takes two objects, and combines them to produce a third object. For example, addition is an operation on (for example) the real numbers; if I have two real numbers like $1$ and $2$, addition combines them to form $1 + 2 = 3$.

The quotation in bold is essentially saying that any operation can be written as a function whose domain is a cartesian product space. Using my example, one can represent addition as a function on the set of pairs of real numbers $$f_+ : \mathbb{R}\times\mathbb{R} \rightarrow \mathbb{R},$$ whose action on pairs of numbers is to add them: $$f_+(x,y) = x + y.$$ (Note: when your textbook says operation, they really mean "binary operation". In general an operation can take $n$ inputs)