Horgan was born in Hackney, London, England. Her mother, Ursula (née Campbell), is Irish, from County Kildare, and whose parents before her originated from Midfield, County Mayo. Her father, John Horgan, is from New Zealand, and ran a pub. When she was four years old, Horgan's parents moved the family to Bellewstown, County Meath in Ireland, to run a turkey farm.
One of five siblings, in interviews Horgan has described her childhood as happy. She has also spoken fondly of growing up on the farm, where she helped with plucking the turkeys: “you pluck down, not up," she once told an interviewer.
Horgan later used her childhood experiences for the semi-autobiographical short film The Week Before Christmas for Sky Arts 1.
Horgan went to the Sacred Heart convent school in Drogheda, which she described in an interview with The Observer in December 2012 as an unhappy experience. “I didn't enjoy it at all," she said.
Horgan is best known for the comedy series Pulling (2006–09) and Catastrophe (2015–2019), both of which she starred in and co-wrote. She also created the HBO comedy series Divorce (2016–2019).
Horgan won the 2008 British Comedy Award for Best TV Actress for Pulling, while the show's 2009 hour-long final episode won the British Comedy Award for Best Comedy Drama.