You can enhance your dragons by using relationship or enhancement points.

Enhancing a dragon increases its HP, ATK, and DEF stats.

Due to the high gold cost of enhancing dragons, I suggest only doing this in late-game. When you move on to enhancing your dragons, you should work on your main attackers first, as they are the ones that benefit the most from the stat boost.

Your supports may not need enhancement at all, though you may wish to enhance your primary healers.

This page details the cost of enhancement for each rarity of dragon.