The Gemara in Shabbos (119b) teaches:
אמר ר ב חסדא אמר מר עוקבא כל המתפלל בערב ש בת ואומר ויכולו שני מלאכי השרת המלוין לו לאדם מניחין ידיהם על ראשו ואומרים לו וסר עוונך וחטאתך תכופר - Rav Chisda said that Mar Ukva said: One who davens on Shabbos evening (Friday night) and recites “Vayechulu”, the two ministering angels who accompany the person at all times place their hands on his head and say to him: “And your iniquity has passed, and your sin has been atoned”.
The question is, which sin is the Gemara referring to? The Ritva, Shiltei Gibborim, and Da’as Zekeinim MiBa’alei Tosfos (Bereishis 2:1) all explain: If one doesn’t recite “Vayechulu” on Friday night, he is withholding eidus [testimony], and one who withholds eidus violates the prohibition of אם לוא יגיד ונשא עוונו – “If one doesn’t testify, he carries sin”, therefore, when one says “Vayechulu”, the malochim say: וסר עוונך – “your sin (of withholding eidus) has been removed”.
We see that the recitation of “Vayechulu” is considered proper eidus, as if not, how can one violate the prohibition of אם לוא יגיד ונשא עוונו – “If one doesn’t testify, he carries sin”.
Every erev Shabbos after chatzos [midday], the Orach Chaim HaKodosh would learn Hilchos EIdus to help prepare himself to give eidus at the beginning of Shabbos about the Creation of the Heavens and the Earth (cited in his Haggadah Shel Pesach pg. 12).
Although we mentioned from Rishonim that reciting “Vayechulu” atones for the sin of withholding eidus, it’s also clear from the poskim that it atones for other sins as well.
The Teshuvas HaGeonim cites the Yerushalmi as a source for the Chazal which says that reciting “Vayechulu” brings atonement: It says the word “asher” by porah adumah and it says the word “asher” by “Vayechulu” (in both places it says the word “asher” three times). We learn from here that just as the porah adumah brings forgiveness and purity, so does the recitation of “Vayechulu”.
The Kaf HaChaim (268:34) adds: The word “asher” appears three times by porah adumah, and by “Vayechulu”, therefore, we say it three times (see Elyah Rabbah 268:12).