Hesychasm encourages the use of the Jesus Prayer in combination with a series of physical and mental techniques to silence the mind and make still the body, while aiming at union with God.
A hesychast is one who strives to enshrine what is bodiless within the temple of the body, paradoxical though this may sound. A hesychast is one who says, 'I sleep but my heart is watchful' (Song of Songs 5:2). Close the door of your cell to the body, the door to your tongue to speech, and your inner gate to evil spirits. (St. John Klimakos, The Ladder of Divine Ascent, Steps 27 and 26 as found in The Philokalia, vol. 4, p. 200.)
Hesychasm as a way of life involves the manifestation of silence not only in terms of the mouth, but in terms of the mind and the entire body. As the last sentence above indicates, closing the door to the body means mastering the physical self (i.e., controlling the need to eat, sleep, and more) and the emotions (i.e., controlling the temper, seeking humility, learning patience, and more). Closing the door to the tongue means silencing our voices and mastering our words when speaking. Closing the door to the inner gate of evil spirits means working to control what we allow inside of ourselves. This is about making our lives simpler, more focused on God, and seeking prayer more intently and intensely.
Put differently, hesychasm is about living, working, and praying in an environment of peace within and without, by controlling the intellect ("For if the hesychast does not enclose his intellect within his body, how can he possess within himself the One who is invested with the body and who as its natural form penetrates all structurally organized matter?" [St. Gregory Palamas found in The Philokalia, vol. 4, G.E.H. Palmer, Philip Sherrard, and Kallistos Ware, ed. and trans. (Faber & Faber, London, 1979), p. 336.]), and controlling the body ("Stillness, in accordance with its name, is maintained by means of peace and serenity; for God is peace [cf. Eph. 2:14] beyond all unrest and clamour" [St. John Klimakos, The Ladder of Divine Ascent, Steps 27 and 26 as found in The Philokalia, vol. 4, p. 278.]).
Bodily control during prayer has enormous implications to our faith life more broadly speaking.
"This control of the breathing may, indeed, be regarded as a spontaneous consequence of paying attention to the intellect; for the breath is always quietly inhaled and exhaled at moments of intense concentration, especially in the case of those who practice stillness both bodily and mentally. Such people keep the Sabbath in a spiritual fashion and, so far as possible, they rest from all personal activities; they strip their soul's powers free from every transient, fleeting and compound form of knowledge, from every type of sense-perception and, in general, from every bodily act that is under our sway, and, so far as they can, even from those not entirely under our sway, such as breathing" (St. Gregory Palamas found in The Philokalia, vol. 4, p. 337).
The second half of this quote is particularly important to our study here. In it, St. Gregory is explaining that those who can achieve some level of silence and stillness in their lives tend to be able to keep the Sabbath properly. Here he does not only mean the actual outer observance of the Sunday Liturgy, but also the inner observance of the Sabbath (i.e., interior prayer stills the soul, mind, and body, helping the person to enter into spiritual rest).
The good news is that if we can get a hold of our lives in this way, we will find ourselves growing closer to God.
In those who have made progress in stillness all these things come to pass without toil and anxious care, for of necessity they spontaneously follow upon the soul's perfect entry unto itself. But where beginners are concerned none of them can be achieved without effort (St. Gregory Palamas found in The Philokalia, vol. 4, p. 337).
And while we cannot achieve this state of mind and body very quickly, if we show ourselves to patient, the fruits of our efforts will be known.
Patient endurance is the fruit of love, for 'love patiently accepts all things' (1 Cor. 13:7), and teaches us to achieve such endurance by forcing ourselves so that through patience we may attain love and this is a case in point (St. Gregory Palamas found in The Philokalia, vol. 4, p. 338).
Thus, the explicit decision to seek silence and practice stillness -- and if we do so with patience, endurance, and the help of the Jesus Prayer -- we will find in ourselves a new sense of what love really means. And if we ground all things in life in that love -- this hesychastic love -- we will be lead to a truer, more loving, and deeper union with God in this life and in the next.