Once you have the Boss Horn, and upgraded it to level 2 (you will need Town Hall level 6 for this upgrade), you can summon a boss for a boss battle. When you Boss Horn is level 2 you will see the summon boss symbol at the top right of the game screen. Tap it top start the boss battle process.
In a boss battle all of your hunters get involved to try to defeat the summoned boss within the set time period.

After the boss battle there is a 20 minute cooldown period as your horn needs to assemble before you can blow it again! The Boss Battles are really difficult and you will need a high level and well equipped team to defeat any boss / even the first one.
You can however go back Difficulty Levels to try easier bosses which may work out better for you if you are struggling. Alternatively you can wait a while, upgrade your hunters and their weapons and armor and retry at a later date.