I never knew anything about mindfulness before I started with my current T. This concept, as well as meditation and encouraging me to take yoga are the best things she's done for me!
I've read a few books about it, so could you please post the one your T recommended?
To me, mindfulness means that I am aware of the beauty around me. I am doing that more and more. I notice the colors in nature: the brown bark of the trees, the green leaves, the blue sky, the clouds, if any, and the green grass. I pay attention to sounds that I enjoy, smiles of my family, and anything I'm doing. The idea is to focus on the present, not the past or future. To be totally in the "now". Then you can't worry about the past or the future. I go to a lake and really take in everything I love about it.
You can be mindful with anything to make it more pleasurable, even doing dishes or laundry! It has nothing to do with thinking about yourself; in fact, when I'm being mindful, I DON'T think about myself. It's a way to go beyond thinking of yourself.