Edom was a nation that stood as one of the enemies of the Kingdom of Judah. Obadiah reveals God’s anger towards Edom and coming judgment for their cruel actions against Judah, such as helping the invaders loot Jerusalem.
The date of writing is unknown. Verses 11 to 14 refer to an invasion of Jerusalem, but there were several of those. The two options that biblical scholars consider most likely are the Philistine invasion in the 9th century BC, or the Babylonian invasion in the 6th century BC and the exile that followed shortly afterwards.