The song is said to have been dedicated by Coldplay frontman, (authors of other wonderful songs such as "The Scientist", "Trouble", "Viva la vida" and "A sky full of stars") Chris Martin, to his ex-wife Gwyneth Paltrow to console her following the death of her father, which occurred following pneumonia contracted during a vacation in Tuscany (Italy)
Literally "fix you" would mean "put it back together", but in the song it has the metaphorical meaning of "heartening", "consoling"
The song is used in the series The O.C., Scrubs and Glee, and even, several times in the Netflix series, La Casa de Papel.