Hi there, yourself! Yes, I think I can help you understand this. I say that because this is one of the terms I have struggled over a long time to understand more deeply in my own journey. As with the elements of the canon itself, hiddenness occurs on a number of levels; all are important; some are more superficial than others and I have tried to understand the ways in which that is true. For instance, the canon calls for stricter separation from the world and that seems to imply the hermit is called to a stricter separation from that required by other Religious, particularly ministerial or apostolic Religious. This separation, to whatever extent and in whatever way it is lived, is defined for religious by their vows and congregational constitutions or Rule. At the most superficial level it implies the qualification of all of one's relationships --- including with power and wealth. We misread stricter separation if our understanding of it stops at a literal closing of the hermitage door on everything outside us or on giving up all relationships, or fail to truly school our hearts with regard to material wealth, and power.
We must penetrate this term (and the others in the Canon) more deeply. Yes, we need to close the hermitage door on certain realities as both a literal and a symbolic way to express all that is essential to this vocation. For instance, this expression helps us embrace the physical silence and solitude that is necessary if one is to eventually understand all the ways we ordinarily give ourselves to false gods or become enmeshed in things that are unworthy of us or our vocation and need to turn instead to the God of Jesus Christ. That growth in perception and integration takes time as we move from superficial to profound understanding and our similar embrace of deeper and deeper truth. Also, earlier forms of meaning (say the literal closing of the hermitage door on relationships and activities) may be more strict in the beginning of our eremitical lives, and may actually need to be relaxed at other points as we embrace less literal or less superficial meanings of the term hiddenness.
For example, learning to turn to the God of Jesus Christ in all things and allow him to shape us into Temples of the Holy Spirit, may require regular work with others (spiritual directors, superiors), participation in some limited form of parish ministry (e.g., teaching Scripture), more intense spiritual direction or inner work with specialists, etc. The functional cloister or anachoresis (withdrawal) of eremitical life remains and contributes to hiddenness, but the constraints on moving outside the hermitage or allowing others into the hermitage may well be relaxed in measured ways as one gives oneself to Christ to be remade more fully and deeply as is possible in specific ways in relationship with some few others. In part this leads me to my understanding of the hiddenness of eremitical life.In all of this what is mainly hidden from the eyes of others is the hermit's relationship with God in Christ and all the work and growth (metanoia) that comes over time as one focuses on this relationship and becoming the person one is called by God to be. Hiddenness is not an end in itself. It serves our relationship with Mystery and for that reason, it is characteristic of assiduous prayer and penance, stricter separation from the world, and engagement with others that grows out of and even intensifies one's silence of solitude. Hiddenness is the most intimate shape of one's personal journey to and in communion with God, but as I have argued earlier, it is an important and derivative value, not a primary one.
For each of us, growth in love of God, and maturation in our relationship with God as we move from darkness to light, from blindness to sight, and from brokenness to wholeness is a hidden process. For most, the relationship with God itself is always hidden --- though one can see symptoms and signs of the quality of the relationship by the way the person loves others, themselves, and the whole of creation. The hermit gives over her entire life to this hidden commitment and growth. She will embrace the elements of Canon 603 in order to be sure she is intensely focused on this commitment alone. She does this for God's sake as well as for her own, for the sake of others, and for the sake of the vocation she has been entrusted with. In some ways, we could say that the hermit lives for God alone so that others may understand that this relationship with God is the primary Good in her life --- and should be primary in everyone's life.The NT saying, [[Seek ye first the Kingdom of God and all these things shall be added unto you,]] is a way of saying, [[ Seek you first and last this relationship with God, and all the other things you need will be added unto you.]] The hermit's witness to this truth is the most vivid one I could imagine here. It witnesses to the completion that is ours in God --- to the eschatological goal of every life. It is a hiddenness that witnesses to the heart, or deepest Being and vocation of the human person. Even the most perceptive spiritual director or Anam Cara cannot completely penetrate the hiddenness of this relationship --- though dimensions of it can be shared.
You also wrote: [[One writer criticizes hermits like you who wear a habit or use Sister as a title or let people know you are a hermit in your blog. She says that is against the hiddenness of the life (though she also has a blog and writes about being a hermit). I think she believes because she insists on being anonymous, that is what makes her life hidden and that you (or anyone calling themselves a hermit) should be the same.]] As I wrote in an earlier piece, [[The authors [of canon 603 and also the CCC passages] did not merely mean it all happens alone (with God) behind closed doors --- though of course it mainly does this; they knew that the real fruit and processes of eremitical life (and thus, of eremitical formation and discernment) have to do with the functions of the human heart being redeemed and transfigured (made whole and holy) by the invisible God within the context of silence and personal solitude in an intimate relationship which is mainly invisible and ineffable.]] Everything about eremitical life is meant to foster and witness to this deep and profoundly relational Mystery which is served by hiddenness and all those elements of desert spirituality that contribute to the vocation's hiddenness.I sincerely hope this is helpful.