Dragon Points are a new ranking system currently only available for Mobile users. It is used to determine your ranking among not only your friends, but the whole world. Currently, the only way to get them is by getting dragons. The amount of dragon points you get from each dragon depends on their category and level. So, the rarer a dragon is, the better it is to earn more points.
The PC version does have stats for this, but not rankings based on it. It also doesn't display your total. You can see how many points each of your dragons has by putting it in the Dragonarium.
NOTE:YOU CANNOT GET ANY SPECIAL REWARDS WITH THE DRAGON POINTS.