Why is there a my $pair? I only see it being used in that one statement.

Um! Cos I made a mistake! It should be @pair and now is:)

Why is there a @pair at the end when the previous line is giving it a value?

The previous line loops a random number of time setting the @pair to succesive key/value pairs from the hash.

Once the loop stops, the last statement becomes the return value for the do block, and so the last key/value pair assigned to the array @pair, get assigned to the variables $name and $url.