The first is feeling confident, believing in yourself, and letting go of any thoughts about "I can't" or "I'm weak" or "I'm not good enough" or "This isn't going to work out well for me." That's the idea Sensei is most likely to talk about when he teaches. When he says "remove impurities," he's talking about something like this, rather than something your Sunday School teacher might have said!
The second way of thinking of positive mind isn't really different, but we tend to think of it as different, because we don't usually pay attention to how the mind and the body are connected. This has to do with the way your state of mind affects your body. You can see directly how this is true. Stand up in your best, natural stance (if you are a Kokikai student you will know what this means, if not, just stand naturally). Now think about what a crummy day you have had. Let negative thoughts about yourself and your life and your world flood your mind. Now check yourself out in the mirror. Next, fill your mind with self-confidence, equanimity, joy, optimism. Look again in the mirror. Do you notice any subtle differences? (If you didn't notice anything you may be too conscious of the experiment.)
So, next time you catch yourself in a really nasty mood, notice your posture. Then do the same the next time you're in a great mood. Want to try something really funky? Try changing your posture and see if it helps change your mood.
We can see the difference in the mirror but there are all kinds of changes going on in the body that we don't see, that are affected by our mental state. Blood flow to muscles, organs and brain; subtle changes in position of muscles; levels of tension; and nerve stimulation are all affected by our mental state. There's lots of people doing research in this area. I barely touched the tip of it in researching an earlier post. Even better than looking for scientific research is to research yourself, and your own body. In your Kokikai practice and your daily life, pay attention to what happens to your body when you change your mental state. Are you more able to react effectively when you are calm and positive? I can tell you from my own "research" that the answer is, "Yes!"