"Define a relation C from R to R"
-a relation is a subset of the Cartesian product of two sets. The two sets in question are R and R (the same set), so C is some set of ordered pairs (x, y) where x, y ∈ R. (meaning x and y are real numbers).
"for any (x, y) ∈ RxR" = "for any ordered pair of real numbers"
"(x, y) ∈ C means x^2 + y^2 = 1" = "an ordered pair being in set C means it satisfies the equation x^2 + y^2 = 1 where x and y in the equation are the named elements in the ordered pair (x and y)"
The only members of this relation C are points (ordered pairs) that lie on the unit circle.