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."