Green’s Dictionary of Slang

(orig. US) the gathering, after a revivalist meeting, of those earnest souls who are ‘anxious for salvation’; thus anxious mourner n., a member of such a gathering.

[1842		Flash (NY) 29 Jan. n.p.: She was conspicuous on the ‘anxious seat,’ loud and fervent in her supplications].
1878		Dly Press & Dakotaian (Yankton, SD) 21 Feb. 4/4: Brother Sharp is holding an anxious meeting [...] It commenced about a week ago, and will continue until every stubborn sinner shall return.
1881		Knoxville Dly Chron. (TN) 20 Mar. 1/1: The anxious meeting was well attended [...] manifestly by seekers of religion.
1895		Topeka State Jrnl (LKS) 27 Mar. 5/2: Many men [...] stay away, ridiculing it and abusing it roundly. They call it [...] ‘Quaker feast,’ ‘anxious meeting’ with other revilements.
1889–90		Barrère & Leland Dict. of Sl., Jargon and Cant I 43/2: Anxious or inquirer’s meeting [...] an after meeting held during a ‘revival’ for the benefit of those who profess to be ‘anxious for their soul’s salvation.’.
1903		S. Clapin New Dict. Americanisms 20: Anxious meeting [...] Anxious mourner. A ‘mourner’ at a revival, urged on by the necessity of seeking salvation.
1914		Day Book (Chicago) 12 June 11/1: The ‘anxious bench’ [...] is occupied by persons who wish to be converted [...] They hold an ‘anxious meeting’, when they are exhorted and prayed over.