The Greek word, as others have pointed out, is ἡσύχιος (hēsychios). It is the quality of ἡσυχία (hēsychia), to which dictionaries, lexicons, and other such resources assign a meaning of "silence" or "quietness".
Although hēsychia appears only four times in the New Testament (and hēsychios two), the word took on tremendous significance later in the Christian east, before and during what has come to be known as the "Hesychast Controversy".
Part of the Hesychast Controversy lay in the disagreement between Barlaam of Calabria and Gregory Palamas. Both were Orthodox Christians who debated over the importance of hēsychia (Gregory Palamas' position) versus a life that favored education and reason over contemplation (Barlaam's position). The debate is summarized:
[Gregory] was initially asked by his fellow monks on Mount Athos to
defend them from the charges of Barlaam ... [Barlaam] believed the
monks on Mount Athos were wasting their time in contemplative prayer
when they should instead be studying to gain intellectual knowledge.
When Gregory criticized Barlaam's rationalism, Barlaam replied
with a vicious attack on the hesychastic life of the Athonite monks.
Gregory's rebuttal was the Triads in defense of the Holy Hesychasts
(c. 1338) ...
A synod held in Constantinople in 1341 also supported St. Gregory's
views, condemning Barlaam. Later, in 1344, [although] the opponents of
hesychasm secured a condemnation for heresy and excommunication for
Gregory, [his] theology was reaffirmed at two further synods held in
Constantinople in 1347 and 1351.
As a result of the dispute, Barlaam left Constantinople and was received into the Roman Catholic Church in 1342, in Avignon.
In a modern English translation of The Philokalia, a compilation of Greek writings that includes works of Gregory Palamas, the editors explain the meaning of hēsychia in the Philokalia's context:
The texts of the Philokalia are, then, guides to the practice fo the
contemplative life ... 'a mystical school of inward prayer' where
those who study may cultivate the divine seed implanted in their
hearts at baptism and so grow in spirit that they become 'sons of God'
(John 1:12), attaining through such deification 'the measure of the
stature of the fulness of Christ' (Ephesians 4:13). The emphasis is
therefore on inner work, on the cleansing of 'the inside of the cup
and plate, so that their outside also be clean' (Matthew 23:46) ...
Atrophy and defeat follow only when outer work is practiced as an end
in itself, and the one thing needful - the inner practice of guiding
the intellect and of pure prayer - is neglected ...
An advanced state which may be acquired through the pursuit of this
path is described as hesychia, a word which not only bears the sense
of traquillity and silence (hence our translation: stillness) but also
is linked through its Greek root with the idea of being seated, fixed,
and so of being concentrated. It is therefore fitting that from this
word should come the term hesychasm, frequently applied to the whole
complex of theory and practice which constitutes the path itself.