Adam Kadmon means "the first Man," the primordial Man. In the narrative of Etz Chaim, he is the first figure that proceeds from the Infinite, before any world that can be named. Gate 3 of Etz Chaim, a summary of the order of emanation written by Chaim Vital, says it this way: from the Infinite "there first unfolds, through its mediation, Adam Kadmon." And since he is only second relative to Ein Sof, the text adds, he may even be called "Adam of Beriah," although he precedes Atzilut.
Why a man? Because, according to the Ari, the whole emanated reality has the form of a person. The same passage concludes: the Infinite is "the soul of the soul," and He emanated from Himself "a single Man who includes all the worlds." His essence, made of the levels of the soul, is called Adam Kadmon; his body is Atzilut; his garments are the three worlds Beriah, Yetzirah and Assiyah. Adam Kadmon is also, says the text, the tip of the yod in the four-letter Name: a stroke so fine that it is barely a letter, set above the four letters that carry the four worlds.
Gate 42 makes him the crown of the whole. Just as each world has a Keter above its Sefirot, Adam Kadmon is "Keter of the four worlds," the root of their souls, their bodies, their garments and their dwellings. He is a fifth dimension, intermediate between these worlds and Ein Sof. Seen from Atzilut, his light is even called Ein Sof: each level seems infinite to the one standing below it.
What comes forth from Adam Kadmon is described with images of the face. Gate 3 speaks of worlds named sight, hearing, smell and speech; Chaim Vital writes elsewhere that the mouth of Adam Kadmon brings forth the world of the Akudim, and that the "kings" of the world of the Nekudim come forth from his eyes. Do not take these words physically: they are ways of naming degrees of revelation, from the most inward to the most outward.
Cordovero does not use this name in the same way. In the Pardes Rimonim, under the entry "Adam," he quotes the Tikkunei Zohar: there is no Sefirah that is not called Adam, "but the first Adam, supreme above them all, is Keter Elyon." For him, Adam Kadmon is the supreme crown itself, called primordial "because it precedes all of emanation." The Ari, for his part, places Adam Kadmon above all of Atzilut, Keter included. Keep what the two readings share: the first name given to what comes forth from the Infinite is "Adam," man.