It all depends on the context. Sacrifice can in some circumstances mean giving something dear to us to the Divine.
Yajna, the fire sacrifice, is the central ritual of the Vedic
sacrificial cult. The basic idea of Yajna according to the Vedic
ritualists was that man can have a happy and prosperous life only if
he lived in harmony with his environment, consisting of Nature and the
Devas who control the forces of Nature. Man gets his progeny and his
sustenance as the gifts of Nature and he should express his thanks to
the Devas. Man is required to make an offering of thanks-giving to the
Devas a share of the good things of Nature which he gets by their
goodwill. This offering is made through fire which is the link between
man and the Devas. This thanks-giving takes the form of ritualistic
fire sacrifices with offerings of commodities and utterance of Vedic
hymns. Proper performance of these Yajnas or sacrifices secures the
goodwill of the Devas through which man's survival and sustenance is
assured. Later on in Chapter 4 the Gita itself speaks of other Yajnas
(Dravya-yajna, Pranayama-yajna, Tapo-yajna, Svadhyaya-yajna and
Jnana-Yajna) of which the fire sacrifice is only one. Thus in the Gita
view Yajna ultimately is a symbol for all the moral and spiritual
effort of man for his higher evolution.
REF: adopted from the commentary of Swami Tapasyananda on Srimad Bhagavad Gita.
It means differently in the spiritual sense.
In the spiritual sense... sacred has a different meaning - it does not
so much indicate giving up what is held dear as an offering of
oneself, one's being, one's mind, heart, will, body, life, actions to
the Divine. It has the original sense of 'making sacred' and is used
as an equivalent of the word yajna. When the Gita speaks of the
'sacrifice of knowledge', it does not mean a giving up of anything,
but a turning of the mind towards the Divine in the search for
knowledge and as an offering of oneself through it. It is in this
sense, too, that one speaks of the offering or sacrifice of works ...
the European sense of the word is not the sense of the word 'Yajna'
or the sense of 'sacrifice' in such phrases as the 'sacrifice of
works'. It doesn't mean that you give up all works for the sake of
the Divine - for there would be no sacrifice of works at all.
Similarly the sacrifice of knowledge doesn't mean that you painfully
and resolutely make yourself a fool for the sake of the Lord.
Sacrifice means an inner offering to the Divine and the real spiritual
sacrifice is a very joyful thing. Otherwise one is only trying to make
oneself fit and has not yet begun the real Yajna.
Commentary by Sri Aurobindo on the Gita 3.9