Pokémon League, also previously known as Monster League is a daily game mode where you have 15 islands to defeat, each island having a real player but with modified power.
On Normal Difficulty, each island that you win gives you rewards like Attribute Stones, Tickets for Monster Myst, League Coins and others.
League coins can be used on League Store.
If you are having problems defeating the trainers, there's also the option of buying a Mercenary Pokémon. A Mercenary is a pokémon that your guild mates have in the Lending Section of the guild.
A Mercenary costs 100k gold, and you can use it for the remaining of your battles on that day. But sadly you cannot use the auto funcion when purchasing a Mercenary. Keep in mind that you can only buy Mercenary pokémon that are the same level as your character level, or bellow. You can't buy Mercenary pokémon that are higher level than your character.
On Hard Difficulty, as the name suggests it's obviously harder, but provides better rewards.
The main reward that players aim for in this mode are the Pack Cards (Blue, Purple and Orange). Those Pack Cards contain Friendship Cards that can be used in the Albums to increase the power of all your pokémon.
Every 5 Islands that you defeat, you can open a Reward that can contain those Card Packs. You can also buy more Rewards for Diamonds.