The song was written by Rosalía, reggaeton veterans Chris Jedi, Gaby Music, and El Kagueto del Guetto, along with Motomami producers David Rodríguez, Noah Goldstein and Dylan Patrice.

"Despechá" is a mambo track, with merengue and electropop elements, about "the joys of leaving work and toxic men behind to hit the club.

[3] In March 2022, Rosalía released her third studio album Motomami, which saw a departure from the new flamenco sound of its predecessor and an embracement of Latin music in an avant-garde and experimental key.

[9] During the medley and "Despechá", Rosalía brought onstage twenty fans previously selected by her team to dance with her, making the performance a highlight within the show.

Described by Pitchfork as "a wonder of efficiency, flitting back and forth between two springy piano chords as it rides an equally fleet percussive rhythm", the song is about leaving work and heartbreak behind to have fun with one's friends in the club and see life in the most hedonist way possible.

I'm grateful for having been able to travel in recent years and have learned from music from other places including the [Dominican Republic], where artists like Fefita la Grande, Juan Luis Guerra, and Omega have inspired me and without them this song would not exist.