Battle Tower is a game mode with 80 floors where you can fight different players every day, with modified powers and difficulties: Easy, Normal and Hard.
Every 2 floors there's a new battle, but every other 2 floors there's either a Buff that applied only inside the Battle Tower or a Chest with rewards.
Each Successful battle will award you with Points and Coins. Points are used in order to calculate your rank compared to the other players in your server, but also to obtain Score Rewards:
On the other side, the coins that you win are used to purchase Buffs on the Buff floor, like restoring HP of your pokémon or simple a buff in your stats.
The higher your floor, the more power the enemies have. But the higher floor you achieve, the more floors you can skip without battling the next day.
For example, since the max floor is 80, if you manage to complete all the 80 floors today, tomorrow you will skip 64 floors, starting your first battle on floor 65 instead of floor 1.
Battle Tower has 2 difficulties, Normal and Hard (Challenge).
On the Normal difficulty, the main resource that you obtain there are Talent Points which are used in the Talent Tree.
On the Hard difficulty, your main resources that you obtain are things like Ribbon Chests where you can obtain Ribbons and also other items to power up your Ribbons