Visarjana means "dismissing" in Sanskrit.
The sixteenth and last upacharas ("offerings")
offered to a god as part of devotion, based on the principle of treating the
deity as a valued guest.
As the last act of devotion, the devotee (bhakta) grants the
god permission to depart.
Although the phrase dismissal seems arrogant in any
conversation with a god, it really relates to the parting remarks that one
would give to a leaving guest.
The fundamental aim here, as with other upacharas, is to
demonstrate one's devotion for the god by ministering to the deity's needs.
You may also want to read more about Hinduism here.
Be sure to check out my writings on religion here.