I have suffered major depression in my life, and I am at the stage that I can manage it myself. I say this because I don't believe that depression can be cured totally, only managed.
I started to look online for help and found a great online CBT course on the BBC website. I did the exercises and this helped me understand what CBT is all about. It is a slow process.
I was fortunate that I lived in a country where help was more than available. I cannot imagine that 6 sessions can tackle such a huge problem. It only scratches the surface. I also agree that you need to "gel" with the therapist to achieve the best results.
I have found this page, and have looked at the step 1, and I think this is quite a good explanation of what happens in CBT. I don't have time today, but I will have a read of the site to see if there is anything written there that I think might help you to understand it better.
CBT self-help programmes
My partner was also diagnosed with depression last year and couldn't work for a while. He had a great therapist that spoke of this Mindfulness that was mentioned before (the new term for CBT?) and this did help him enormously. BUT, he was only entitled to 6 sessions, and I don't believe that was enough. We are still working through his issues, and I think that if I hadn't had similar experiences, we would no longer be together. It's hard being in a depression but it is also very hard to support someone suffering too.
I do hope that you get something from your therapy. But if not, I would suggest that this is not the right time for it and try again at a later date.
Best wishes