Jagger and Richards adopted this nickname after a holiday cruise to Brazil, which they took in December 1968 and January 1969 with Marianne Faithfull and Anita Pallenberg (their girlfriends at the time). An older English couple on the ship kept asking Richards and Jagger who they were. When they declined to reveal their identities, the woman reportedly kept asking, "just give us a glimmer" (meaning "give us a hint about who you are"); this amused Jagger and Richards.
The first Stones album produced by Jagger and Richards under this pseudonym was It's Only Rock 'n' Roll (1974). The Glimmer Twins were the sole credited producers for the band's studio and live albums from then, up to and including Still Life (1982). Starting with Undercover (1983), the Glimmer Twins have shared production credit for the Rolling Stones albums with other producers, most frequently Don Was (five times) and Chris Kimsey (three times).
Besides their production work for the Rolling Stones, Jagger and Richards also used the Glimmer Twins for their co–production credit on Peter Tosh's album Bush Doctor (1978). A rare exception was John Phillips's album Pay Pack & Follow (recorded 1973–1979, released in 2001), for which Jagger and Richards were credited as producers under their own names.
The above is an edited version of the explanation given on Wikipedia.
© Haydn Thompson 2020