Swaha is chanted at the end of rituals, especially those that involve fire and elaborate mantras and chanting. During yagnas, hawans, and kapur (camphor) rituals, we end our offerings with ‘Swaha’. And to ‘Swaha’ something, means to offer it whole and soul, and be in complete surrender of that object, thing, or feeling. Swaha is equated to offering something to the Gods or sacrificing something, which could also be a material wish or want.
In Vedic rituals, Swaha is said when something, usually ghee or other offerings, is poured into the sacred fire.
When we say Swaha as a part of mantras, it means we are sacrificing and offering something by giving up all our attachments.