Although you can see that the glass is half-empty, you chose to see it in a positive way. It is still half-full, anyway. The absence of half of the volume of water didn't even bother you. What mattered was that it still contains water. If this is how you answered the question above and how you justified your answer, then you have a positive way of thinking.
Positive thinking is a way of looking at the brighter side of life. Everything is good, beautiful, and light. There are no worries, problems, or fears. In short, all you see and believe in is, well, positive. I guess that is already the most suitable word in describing this way of thinking, which is why it is the term being used.
This kind of thinking is very powerful in that if you think that you are going to pass an exam, you are going to pass; if you think that you will get noticed by your crush, you will get noticed; if you think you will get promoted at work, then you will get promoted. This is how powerful the mind is, particularly positive mind. Even the famous Clint Eastwood believes in this general truth that he quoted, If you think it is going to rain, it will.
So, how does the power of positive thinking works? How can it create reality? Do we only have to think of positive things and then will it happen right away? That positive thinking really is powerful may be somehow hard to believe at first, that is why we may ask certain questions like those above. Because the mind is working on the information you send it, positive thinking leads to positive reality. This is how it works. Yes, we do have to really think of positive things. But it does not stop there.
Remember the ever-famous cliché Do your best and God will do the rest? You know, it true. Aside from believing in and having faith in something we want to happen, we have to do something about it. You can't get a perfect score in an exam just by sitting on the couch and watching TV days before taking it, can you?