There is more than one artist with this name, including:
1) The Springfields was a British pop-folk vocal trio of the early 1960s remembered as the launch pad for singer Dusty Springfield.
2) The Springfields was an American indie-pop band from New England active between 1988 and 1991.

1. The Springfields was a British pop-folk vocal trio in the early 1960s, who had success both in the UK, USA and Ireland, but are now best remembered as the launch pad for singer Dusty Springfield.
The trio formed in 1960, when Mary "Dusty" O’Brien joined her brother Dion O'Brien and Tim Feild, who had been working as a duo,"The Kensington Squares". Dion became Tom Springfield, and Mary became Dusty Springfield. Feild was later replaced by Mike Hurst.
Tom Springfield was a songwriter and arranger with a wide knowledge of folk music, and the group had strong vocal harmonies and Dusty’s powerful lead. They were signed to Philips Records and released their first single, "Dear John," in 1961, followed by two UK chart hits with "Breakaway" and "Bambino" – like their other records, produced by Johnny Franz.
In 1962, their version of "Silver Threads and Golden Needles" – which surprisingly was not released as a single in the UK - reached the US Top 20, the first single by a British group ever to do so (predating the Tornados’ “Telstar” by two months, and the Beatles by 15 months). The record also reached # 1 in Australia.
At the end of 1962 they had the biggest hit of their career in Britain, "Island of Dreams", which reached # 5 in the charts, as did the follow-up "Say I Won’t Be There". By this time the Springfields were one of the most popular groups in the UK. However, Dusty Springfield felt increasingly hemmed in by the group's image as a folk act and Tom's lead role within the trio, and towards the end of 1963 decided to leave for a solo career.
Tom Springfield and Mike Hurst also developed successful careers in the music industry, while Tim Feild (as Reshad Feild) later became a prominent mystic and writer.

2: The Springfields was an American indie-pop band from New England, USA, related to Choo Choo Train and Velvet Crush. They released several 7" singles between 1988 and 1991 on Bus Stop, Sarah, Seminal Twang; with Matthew Sweet producing their Sunflower single.
Discography:
Sunflower (7") 1988 on The Bus Stop Label - BUS 1
Sunflower (7") Jul 1988 on Sarah Records - SARAH 010
Mini-LP [unreleased] (LP) on Subway Organization - SUBORG 06
Wonder / Tomorrows Ends Today (7") Feb 1991 on Sarah Records - SARAH 040
Reach For The Stars (7") 1991 on Summershine Records - SHINE 005
She Swirls Around Me (7") 1991 on Picture Book Records - PB005
Tranquil (7") on Seminal Twang Records
They were also featured on many Sarah compilations including the label's final release There and Back Again Lane.
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