The phrase (not) to go gentle into that good night, also (not) to go gently into that good night, means (not) to give up or acquiesce, especially to death, without a struggle.

It alludes to Do not go gentle into that good night, used as the title of, and in, a poem by the Welsh poet Dylan Marlais Thomas (1914-53)—this is the first stanza:

Do not go gentle into that good night,
Old age should burn and rave at close of day;
Rage, rage against the dying of the light.

First published in Botteghe Oscure: quaderno VIII, II semestre 1951 (Roma: Arnoldo Mondadori), Do not go gentle into that good night appeared in 1952 in two collections of poems by Dylan Thomas:
– In Country Sleep and Other Poems (New York: New Directions), published on 28^th February 1952 in a limited signed edition of 100 copies, followed by a trade edition;
– Collected Poems 1934-1952 (London: J. M. Dent & Sons Ltd.), published on 10^th November 1952.

(The publication details are from the website Dylan Thomas.)

Dylan Thomas’s phrase has been misquoted as Do not go gently into that good night—as in the obituary of the poet, published in the Los Angeles Times (Los Angeles, California) of 10^th November 1953:

Among his best-known poems is “Do Not Go Gently into that Good Night.” It expresses the need for a purposeful and positive attitude toward death, rather than a defeatist one.

The earliest use of the phrase that I have found is from the review by Richard M. Brace of “Napoleon at St. Helena: The Journals of General Bertrand from January to May of 1821,” deciphered and annotated by Paul Fleuriot de Langle, translated by Frances Hume. [Double-day, $3.75.]—review published in the Chicago Daily Tribune (Chicago, Illinois) of 11^th May 1952:

The literature on the “Little Corporal” is great. […] Each generation since 1821*, when the Little Corporal did “not go gentle into that good night,” has had its say on what he stood for and what he stood against.

(* Napoléon Bonaparte, Emperor of the French as Napoléon I from 1804 to 1814 and in 1815, was born in 1769 and died in 1821.)

The second-earliest use of the phrase that I have found is from Vista and Vision, by the English theatre critic and author Kenneth Tynan (1927-80), published in The Observer (London, England) of 1^st April 1956:

Our modish playwrights see their heroes as islands, doomed to be swamped by an impersonal and vanquishing sea. Their prevalent theme is frustration, the hero is either defeated by society or reduced by it to a negative conformity. What has vanished is the positive concept of men living fruitfully together. Modern heroes die sadly in the dark; they “go gentle into that good night,” a pitiful spectacle which has bred in modern audiences an appetite for pathos that amounts to an addiction.

The earliest use that I have found of the variant with gently is from the column Bookman’s Corner, by Walt McCaslin, Daily News Book Reviewer, published in the Dayton Daily News (Dayton, Ohio) of 2^nd November 1958—Walt McCaslin was reviewing The Bathtub Hoax and Other Blasts and Bravos, a collection of columns by the U.S. journalist, essayist, satirist and critic Henry Louis Mencken (1880-1956):

He [= H. L. Mencken] saw life as a gay and gaudy adventure—a wholly salubrious experiment when carried on in the spirit of intellectual freedom. Mencken never betrayed his credo. He went “gently into that good night” after a shrimp dinner and a pleasant hour with his friends, without any of the depressing deathbed repudiations that come from the dour and the pessimistic.

 

Dylan Thomas at Laugharne, in Wales, where he spent the last four years of his life—photograph from The Philadelphia Inquirer (Philadelphia, Pennsylvania) of 11^th June 1989: