In order to upgrade your dragon, you need to have enough tokens, which is indicated by the number next to their ranking. 

 

Keep in mind that you can earn tokens for dragons you do not own yet. If it says "get this dragon", instead of "upgrade", it means that you need to own this dragon on Berk first in order to utilize it further.

 

Upon upgrading your dragon, it will gain more health, attack power, defense and speed. 

At some point you will need to upgrade your dragon on Berk first, before you can upgrade it for the brawl.