This is what we found on Wikipedia regarding the The Swell Season:

The Swell Season is a folk rock duo formed by Irish musician Glen Hansard and Czech singer and pianist Markéta Irglová. "The Swell Season" name is derived from Hansard's favourite novel by Josef Škvorecký from 1975 bearing the same title. Their debut album, released in 2006, carried the same name.

The duo rose to prominence following the success of the 2007 film Once, directed by John Carney, in which the pair starred depicting a dramatised version of their own musical pairing. Their song "Falling Slowly" from the film's soundtrack took the Oscar for Best Original Song at the 80th Academy Awards. They increasingly referred to themselves as "The Swell Season" in promotion of their performances until it became the formal name of their collaboration in 2008. (They still used their separate names when they contributed their cover of Bob Dylan's "You Ain't Goin' Nowhere" to the 2007 soundtrack of I'm Not There.)