Partzuf means face, figure. In Etz Chaim, the word designates a Sefirah that is no longer a mere point, but a complete structure of ten Sefirot, with a head, a body and limbs.
To understand why, go back to the breaking of the vessels. At the beginning, the ten points of the world of Tohu were each a vessel too small for its light. Shaar HaKlalim tells what followed: seeing that the vessels had broken because they could not bear the great light, the Emanator wished to repair all the worlds so that they could carry it, through the expansion of the light and its distancing, so that it would arrive more veiled. Then, from the point of Keter, He made a complete partzuf of ten Sefirot, which had been contained in it from the start and which He brought into actuality: this was Arich Anpin. From the point of Chokhmah, Abba; from Binah, Ima; from the six broken points joined together, Zeir Anpin; and from the tenth point, the Nukva.
Etz Chaim sums up the principle in one sentence: "the whole essence of the Tikkun is the enlarging of the vessel and its becoming a partzuf, so that the light diminishes, the vessel widens, and it can bear it." Elsewhere, Chaim Vital specifies: the light of the upper levels was too great for the lower ones; once organized into a complete partzuf, it passes through screens and garments, thickens, diminishes, and flows through openings, channels and very fine hairs. Only then can the lower ones receive it.
What makes something a partzuf? Chaim Vital answers: fewer than three Sefirot is not called a partzuf, for three lines are needed, the right, the left, and the middle one that decides. A partzuf is a balanced figure, never a single quality. The five main partzufim correspond to the letters of the Name: the tip of the yod for Arich Anpin, the yod for Abba, the first heh for Ima, the vav for Zeir Anpin, the final heh for the Nukva.
Why were the partzufim not made at once? Shaar HaKlalim asks the question and answers: so that man would have choice and will. Evil comes from the broken vessels, good from the great light; without this there would be only good, and neither reward nor punishment. The righteous, through good deeds, raise the fallen sparks.
Cordovero knew these names from the Idrot, but he did not organize them this way: for him, Arich Anpin is Keter, Zeir Anpin gathers eight Sefirot, from Chokhmah to Yesod, and the Nukva is Malkhut. Keep the Ari's lesson: a light that finds no form shatters; a light that finds a face can be received.