Symbolism, Imagery, Allegory
Assumption is the small town where Calixta and Alcée met up and shared kisses long ago. It's also, tellingly, where they did not give in to their carnal desires completely – they never had sex there. The name Assumption has religious connotations that remind us of virginity and chastity. In Christianity, it's a reference to a specific event: the Virgin Mary's ascent to heaven after she dies.
Instead of having sex in a place associated with virginity, the place Calixta and Alcée finally consummate their feelings for one another is in Calixta's home. However, it's the memory of their time in Assumption – a place reminiscent of chastity where they couldn't be together – that sparks a more mature, adult interlude between them.
For more on the connection of Calixta's home and her sexual encounter with Alcée, see "Setting."