Swayamvara Parvati Homa is performed to appease
Goddess Parvati - the Mother of Goddess, for removing various obstacles that delay any marriage.
Legend says that
Shakti or the Divine Mother took the incarnation of Goddess Parvati in order to get married to
Lord Shiva. Lord Shiva himself gave the Swayamvara Parvati Mantra to Goddess Parvati, which helped Her to join up with her divine consort.
Hence it is believed that performing Swayamvara Parvati Homa will remove the obstacles and delay in marriage and bless the bride or groom with suitable spouse.