The Musaf Service--which is held immediately following the Morning Service) consists of the Musaf Amidah, the cantor's repetition of the Amidah, the avodah — a recounting of the Yom Kippur service in the Holy Temple — and the priestly blessing.
Priestly Blessing
The priests, or kohanim, direct descendants of Aaron, the High Priest, are commanded to bless the Jewish people with a three-fold blessing. It is customary to perform this duty during the Musaf service on festival days. In preparation for the blessing, the priests remove their shoes and the Levites ritually wash their hands, they then gather at the front or by the eastern wall of the synagogue.
During the blessing, one must not gaze at the Priests directly as the Divine Presence rests upon them. It is customary for men to cover their eyes with their prayer shawls, and for women to gaze into their prayer books.
After the blessing, it is customary to thank the Priests with the words, Yishar Koach.
Re: Birchas Cohanim You're right that they are simply fulfilling a commandment. However, commentaries point out that this is similar to what we find in the Talmud Bava Kama 92b "Raba [further] said to Rabbah b. Mari: Whence can be derived the popular saying, 'Though the wine belongs to the owner, the thanks are given to the butler'? He replied: As it is written (Numbers 27:18-20), "And thou shalt put of thy honour upon him, that all the congregation of the children of Israel may hearken, and it is also written (Deuteronomy 34:9), "And Joshua the son of Nun was full of the spirit of wisdom, for Moses had laid his hands upon him; and the children of Israel hearkened unto him...."
I.e. Though the spirit of wisdom belongs to G-d it is nevertheless ascribed to Moses. Same too here, we thank the Kohanim, even though the blessing is from G-d.