On the LP, Perfection is a word used to describe a state of existence whereby an individual is fully aligned, fully Activated, and consequently perfectly and permanently Connected to their own Highest Self. When one has perfected the Physical Unit, one is capable of strong, pure, and persistance Connection.
"In treading the Path, the Sufi ascends until perfection is reached, and in the perfect sain, God and [individual ego] become one again. Abd Al-Kaim Jili 
The "perfect man" is a concept in Islam referring to someone who has "purified" the self from ailments, complexes, ignorance, deviations, etc. 
In Christianity, the concept of perfection refers mostly to alignment.
Maria Sabina, a Mazatac Wise One/Shaman, after many years of connection practice, claims perfection. "I had attained perfection. I was no longer a simple apprentice. For that, as a prize, as a nomination, the Book had been granted me. When one takes the saint children, one can see the Principal Ones. Otherwise not.
In esoteric and exoteric religious traditions, the notion of perfection is often corrupted and cast as part of the Fool in School archetype, which says we need to suffer, meet challenge, and learn lessons in order to achieve perfection. "...perfection is indeed the goal of every human life but that it may take many lifetimes to achieve...Failing to reach full realization in this life doesn't damn you to perdition; it simply means you'll have to come back again and again until you get it right."
- Margaret Smith, Readings from the Mystics of Islam (Westport, CT: PIR Publications, 1994), https://amzn.to/2MdrfqB
- Mutahhari, Murtadha. Perfect Man. Translated by Dr. Alaedin Pazargadi. Iran: Bethat Islamic Research Center, Unknown. https://www.al-islam.org/perfect-man-murtadha-mutahhari.
- Maria Sabina quoted in Estrada, Alvaro. Maria Sabina: Her Life and Chants. Translated by Henry Munn. Santa Barbara, California: Ross-Erikson, 1981. p. 47.
- Smoley, Richard, and Jay Kinney. Hidden Wisdom: A Guide to Western Inner Traditions. Illinois: Quest Books, 2006.