The acme of Selichos is the recitation of the Thirteen Attributes of Mercy, these high points are interspersed all over the prayers, forming a chain of peaks throughout the service. Chazal tell us in Rosh Hashanah (17b) that this precious formula was taught to Moshe by Hashem himself: “The Holy one wrapped himself up as a Shliach Tzibbur and showed Moshe the order of prayer, and told him, ‘Whenever Israel sin, they should perform this order and I will forgive them’”.
Moshe was taught many things by Hashem including the entire Torah but nowhere do we find the particular way in which Hashem attired himself. What is intended by Hashem wrapping himself up like Chazzan? How is this meant to affect our recounting of the Thirteen Attributes?
The role of a Chazzan is very different to that of teacher. An educator imparts his knowledge to the student; the pupil will occasionally question bringing about greater clarity to both the student and the teacher. However even though the exchange is mutually beneficial, it is nevertheless a detached relationship. Not so the function of the Chazzan of a congregation, his is a joint exercise between himself and the people, he is their emissary, praising, pleading and beseeching G-d on their behalf.
When Hashem clothed himself like a Chazzan, He was informing Moshe that this is a joint project, you Moshe will join me in the Thirteen Middos – I will be merciful – together with you, I will be patient – together with you. We will take a trip through these traits together, because to activate the Attributes the people have to emulate these Divine characteristics.
This answer dovetails with another deduction that was shared with me by Rabbi Topp. Hashem told Moshe whenever the Jewish people act out these Thirteen Attributes I will forgive them, The Meforshim point out it is not merely enough to recount them but one has to imitate them.
(Note: The Tomer Devorah gives practical advice on how to emulate the Divine Middos.)