The word Atzilut comes from a verse in Numbers. G-d says to Moses about the seventy elders: "I will draw from the spirit that is upon you and place it upon them." I will draw is veatzalti. Cordovero, in gate 16 of the Pardes Rimonim, devoted entirely to the four worlds, draws the meaning of the word from it: the power of the Emanator passes into the emanated without the Emanator losing anything, "like one who lights a candle from a candle, and the first loses nothing." He also links the word to etzel, "beside": Atzilut designates what stays attached to its cause. The seventy elders drew the holy spirit from Moses and stayed attached to him like the light of the moon to the spark of the sun.
The classic formula comes from the Tikkunei Zohar: in the ten Sefirot of Atzilut, "the King is in them; He and His essence are one in them, He and His life are one in them," which is not so in the ten Sefirot of Beriah. Cordovero reads three united levels in this sentence: Ein Sof, the essence that spreads, and the Sefirot themselves. He draws a consequence for religious life: prayer, blessings and commandments are addressed to this King united with His Sefirot, "to Him certainly, and not to His attributes," except as they are joined to His essence.
Etz Chaim says the same thing in its own vocabulary: "all of Atzilut is complete divinity, for the vessels themselves are divinity," whereas Beriah, Yetzirah and Assiyah are complete vessels, which are not divinity. The Ari links Atzilut to the yod of the Name and to Chokhmah, quoting the Psalm: "You made them all with wisdom." Up to Chokhmah, he explains, the light of the Infinite is revealed without any screen; from Beriah on, it passes only through a screen, and what passes is no longer the light itself but what it engenders.
What does this world contain? For the Ari, its ten Sefirot run from Atik Yomin to the Nukva of Zeir Anpin: it is the world of the partzufim, which the next section presents one by one. The Tikkunei Zohar give an image to place the levels: in Atzilut is "the very image of the King," in Beriah the King's seal, in Yetzirah the imprint of the seal in wax.
Keep what sets this world apart. Cordovero explains that the word Beriah speaks of separation from the source; Atzilut lies before any separation. And he insists: the Infinite has nothing more before Atzilut, nothing less after it. Emanation takes nothing from Him; it only makes what was hidden shine.
