St. Teresa refers to this second degree of prayer as the "prayer of quiet". In this prayer the soul begins to become recollected and then something supernatural happens. She says this is supernatural because the soul in no way can acquire this prayer through its own efforts.
"In this prayer the faculties are gathered within so as to enjoy that satisfaction with greater delight. But they are not lost, nor do they sleep. Only the will is occupied in such a away that without knowing how it becomes captive; it merely consents to God allowing Him to imprison it as one who well knows how to be the captive of its lover."
"All this that takes place here brings with it the greatest consolation and with so little labor that prayer does not tire one even though it last for a long while."
" This quietude and recollection is something that is clearly felt through the satisfaction and peace bestowed on the soul, along with great contentment and calm and a very gentle delight in the faculties."
St. Teresa advises souls in the prayer of quiet to proceed "gently and noiselessly" and to not let the distractions of the imagination and intellect disturb this peace. During this prayer the soul should not go running about with the intellect looking for great concepts; words and reflections to give thanks for this gift; or listing ones sins and faults because they see the gift is unmerited. "One should pay no attention to the intellect, for it is a grinding mill."
The virtues grow incomparably better than in the previous degree of prayer because the soul is much closer to God. "This prayer of quiet is the beginning of all blessings. The flowers are already at the point in which hardly anythng is lacking for them to bud."
(from The Book of Her Life ~ St. Teresa of Jesus)