From Fire Emblem Heroes Wiki

A player uses his or her team to do battle across various maps to earn EXP and rewards.

Story Maps

See also: Story Maps

Here you will learn about the Kingdom of Askr chapter by chapter. These maps have three difficulties. Normal, Hard and Lunatic and each first completion of a map will reward you with an Orb.

Paralogue Maps

See also: Paralogue Maps

These maps are additional story maps featuring characters from the Summoning Focus banner. Like the Story Maps, these have three difficulties and will rewards you with an Orb after completion.

Special Maps

Main Article: Special Maps

Special Maps are specific event maps on rotation or from announced events which can be accessed from Battles > Special Maps. These maps may have special win conditions such as "All allies must survive.", but will include rewards on first completion such as heroes and orbs.

Arena Maps

Main article: Arena: Arena Maps