What does pulling on syrup (in the semi-solid state) do to the texture/taste? I have seen this done at candy shops before, where the syrup is pulled/stretched 10s of times before they are allowed to cool off.

What chemically does this do to the sugar? How does this affect the taste?
It aerates the sugar (you do the same for taffy) - adding tiny bubbles in the final product.  

It makes the finished product lighter and chewier instead of denser and hard.