These are three quotes from the actual Vatican document that I found helpful:
"In such cases, a blessing may be imparted that not only has an ascending
value but also involves the invocation of a blessing that descends from
God upon those whorecognizing themselves to be destitute and in need
of his helpdo not claim a legitimization of their own status, but who beg
that all that is true, good, and humanly valid in their lives and their
relationships be enriched, healed, and elevated by the presence of the
Holy Spirit. These forms of blessing express a supplication that God may
grant those aids that come from the impulses of his Spiritwhat
classical theology calls "actual grace"so that human relationships may
mature and grow in fidelity to the Gospel, that they may be freed from
their imperfections and frailties, and that they may express themselves
in the ever-increasing dimension of the divine love."
"God never turns away anyone who approaches him! Ultimately, a blessing
offers people a means to increase their trust in God. The request for a
blessing, thus, expresses and nurtures openness to the transcendence,
mercy, and closeness to God in a thousand concrete circumstances of
life, which is no small thing in the world in which we live. It is a
seed of the Holy Spirit that must be nurtured, not hindered."
"Indeed, through these blessings that are given not through the ritual
forms proper to the liturgy but as an expression of the Church's
maternal heartsimilar to those that emanate from the core of popular
pietythere is no intention to legitimize anything, but rather to open
one's life to God, to ask for his help to live better, and also to
invoke the Holy Spirit so that the values of the Gospel may be lived
with greater faithfulness."