"Aber du siehst es doch!"
It's almost like a "vocal interference" in English. You know how some people take to using "like" too much in a sentence?
"It's just, like, you know..."
"Doch" is a very nebulous word. Don't fret over it too much. It doesn't drastically change the meaning of sentences it is used within. At least not in any context that I can think of. (Someone feel free to correct me if they can think of an example that proves me wrong.)
When in doubt, omit "doch" when translating the sentence. Then just think of "doch" as a reinforcer to whatever the rest of the sentence means.
Now, to confuse things slightly, when doch is used as a reply to something someone else has said, it is meant as polite disagreement.
"It's a beautiful day to go to the beach!"
"Doch! It's raining!"
@Naaate This blog post should help clarify some things for you: http://yourdailygerman.wordpress.com/2012/02/27/meaning-of-doch/