The chapter takes its title from the discussion of the companions of the elephant whose destruction it relates.
The general who ruled Yemen named Abraha, had built an opulent church in Sana’a in order to divert pilgrims from the Ka’ba in Makka. A narration states that a few members of the Quraysh had gone to Yemen and defiled the church.
When the the visitations to the Ka’ba were not abandoned, he sent an army with an elephant to destroy the Ka’ba. Divinity protected the Ka’ba by sending a swarm of birds that pelted the army destroying them.
This chapter and the next (Al Quraysh 106) are a pair which together are a warning to the Quraysh that they were protected not because of their status but because Allah wished to protect the Ka’ba and to make way for the coming of His final messenger.