Introduction:
That's such a great and important question! For me personally, articulating the definition of this phrase or the description of what I mean by it has been a bit difficult. It is a positive phrase but in some ways I found my own senses of what I meant by this come to real clarity by paying attention to examples of inauthentic eremitical life, individuals who call themselves hermits, for instance, but who, while nominally Catholic, are isolated and/or subscribe to a spirituality which is essentially unhealthy while embracing a theology which has nothing really to do with the God of Jesus Christ. To paraphrase Jesus, not everyone who says "Lord, Lord" actually has come to know the sovereignty of the Lord intimately. In other words it was by looking at what canonical hermits were not and could or should never be that gave me a way of articulating what I meant by "being a hermit in some essential sense." Since God is the one who makes a person a hermit, it should not surprise you to hear I will be describing the "essential hermit" first of all in terms of God's activity.
Related to this then is the fact that the hermit's life is a gift to both Church and world at large. Moreover, it is a gift of a particular kind. Specifically, it proclaims the Gospel of God in word and deed but does so in the silence of solitude. When speaking of being a hermit in some essential way it will be important to describe the qualities of mission and charism that are developing (or have developed) in the person's life. These are about more than having a purpose in life and reflect the simple fact that the eremitical vocation belongs to the Church. Additionally they are a reflection of the fact that the hermit precisely as hermit reflects the good news of salvation in Christ which comes to her in eremitical solitude. If it primarily came to her in another way (in community or family life for instance) it would not reflect the redemptive character of Christ in eremitical solitude and therefore her life could not witness to or reveal this to others in and through eremitical life. Such witness is the very essence of the eremitical life.
The Experience at the Heart of Authentic Eremitism:
Whenever I have written about becoming a hermit in some essential sense I have contrasted it with being a lone individual, even a lone pious person who prays each day. The point of that contrast was to indicate that each of us are called to be covenantal partners of God, dialogical realities who, to the extent we are truly human, are never really alone. The contrast was first of all meant to point to the fact that eremitical life involved something more, namely, a desert spirituality. It was also meant to indicate that something must occur in solitude which transforms the individual from simply being a lone individual. That transformation involves healing and sanctification. It changes the person from someone who may be individualistic to someone who belongs to and depends radically on God and the church which mediates God in word and sacrament. Such a person lives her life in the heart of the Church in very conscious and deliberate ways. Her solitude is a communal reality in this sense even though she is a solitary hermit. Moreover, the shift I am thinking of that occurs in the silence of solitude transforms the person into a compassionate person whose entire life is in tune with the pain and anguish of a world yearning for God and the fulfillment God brings to all creation; moreover it does so because paradoxically, it is in the silence of solitude that one comes to hear the cry of all in union with God.
If the individual is dealing with chronic illness, for instance, then they are apt to have been marginalized by their illness. What tends to occur to such a person in the silence of solitude if they are called to this as a life vocation is the shift to a life that marginalizes by choice and simultaneously relates more profoundly or centrally. Because it is in this liminal space that one meets God and comes to union with God, a couple of things happen: 1) one comes to know one has infinite value because one is infinitely loved by God, not in terms of one's productivity, one's academic or other success, one's material wealth, and so forth, 2) one comes to understand that all people are loved and valued in the same way which allows one to see themselves as "the same" as others rather than as different and potentially inferior (or, narcissistically, superior), 3) thus one comes to know oneself as profoundly related to these others in God rather than as disconnected or unrelated and as a result, 4) chronic illness ceases to have the power it once had to isolate and alienate or to define one's entire identity in terms of separation, pain, suffering, and incapacity, and 5) one is freed to be the person God calls one to be in spite of chronic illness. The capacity to truly love others, to be compassionate, and to love oneself in God are central pieces of this.
The Critical Question in Discernment of Eremitical Vocations:
What is critical for the question at hand is that the person finds themselves in a transformative relationship with God in solitude and thus, eremitical solitude becomes the context for a truly redemptive experience and a genuinely holy life. When I speak of someone being a hermit in some essential sense I am pointing to being a person who has experienced the salvific gift the hermit's life is meant to be for hermits and for those they witness to. It may be that they have begun a transformation which reshapes them from the heart of their being, a kind of transfiguration which heals and summons into being an authentic humanity which is convincing in its faith, hope, love, and essential joy. Only God can work in the person in this way and if God does so in eremitical solitude --- which means more than a transitional solitude, but an extended solitude of desert spirituality --- then one may well have thus become a hermit in an essential sense and may be on the way to becoming a hermit in the proper sense of the term as well.
If God saves in solitude (or in abject weakness and emptiness!), if authentic humanity implies being a covenant partner of God capable of mediating that same redemption to others in Christ, then a canonical hermit (or a person being seriously considered for admission to canonical standing and consecration) MUST show signs of these as well as of having come to know them to a significant degree in eremitical solitude. It is the redemptive capacity of solitude (meaning God in solitude) experienced by the hermit or candidate as "the silence of solitude" which is the real criterion of a vocation to eremitical solitude. (See other posts on this term but also Eremitism, the Epitome of Selfishness?) It is the redemptive capacity of God in the silence of solitude that the hermit must reflect and witness to if her eremitical life is to be credible.
Those Putative "Hermits" not Called to Eremitical Solitude:
For some who seek to live as hermits but are unsuccessful, eremitical solitude is not redemptive. As I have written before the destructive power of solitude overtakes and overwhelms the entire process of growth and sanctification which the authentic hermit comes to know in the silence of solitude. What is most striking to me as I have considered this question of being a hermit in some essential sense is the way some persons' solitude and the label "hermit" are euphemisms for alienation, estrangement, and isolation. Of course there is nothing new in this and historically stereotypes and counterfeits have often hijacked the title "hermit". The spiritualities involved in such cases are sometimes nothing more than validations of the brokenness of sin or celebrations of self-centeredness and social failure; the God believed in is often a tyrant or a cruel judge who is delighted by our suffering -- which he is supposed to cause directly -- and who defines justice in terms of an arbitrary "reparation for the offences" done to him even by others, a strange kind of quid pro quo which might have given even St Anselm qualms.
These "hermits" themselves seem unhappy, often bitter, depressed and sometimes despairing. They live in physical solitude but their relationship with God is apparently neither life giving nor redemptive -- whether of the so-called hermit or those they touch. Neither are their lives ecclesial in any evident sense and some are as estranged from the Church as they are from their local communities and (often) families. Because there is no clear sense that solitude is a redemptive reality for these persons, neither is there any sense that God is really calling them to eremitical life and the wholeness represented by union with God and characterized by the silence of solitude. Sometimes solitude itself seems entirely destructive, silence is a torturous muteness or fruitlessness; in such cases there is no question the person is not called to eremitical solitude.
Others who are not so extreme as these "hermits" never actually embrace the silence of solitude or put God at the center of their lives in the way desert spirituality requires and witnesses to. They may even be admitted to profession and consecration but then live a relatively isolated and mediocre life filled with distractions, failed commitments (vows, Rule), and rejected grace. Some instead replace solitude with active ministry so that they really simply cannot witness to the transformative capacity of the God who comes in silence and solitude, much less the silence of solitude. Their lives thus do not show evidence of the incredibly creative and dynamic love of God who redeems in this way but it is harder to recognize these counterfeits. In such cases the silence of solitude is not only not the context of their lives but it is neither their goal nor the charism they bring to church and world. Whatever the picture they have never been hermits in an essential sense.
Even so, all of these lives do help us to see what is necessary for the discernment of authentic eremitical vocations and too what it means to say that someone is a hermit in some essential sense. Especially they underscore the critical importance that one experiences God's redemptive intimacy in the silence of solitude and that one's life is made profoundly meaningful, compassionate, and hope-filled in this way.