The word sacrifice originates from the Latin meaning holy or sacred. Religion has used the ritual of sacrifice to bring protection (sacrificing a lamb for example) or calling Christ the Divine Lamb for He sacrificed himself for the world.
How shall we understand this at our level? Well, considering that Initiatic Science teaches that we have two natures: a personality (the ego) and an individuality (the higher Self). The personality always seeks its own satisfaction even at the expense of others or the higher Self. Whereas the individuality is always altruist, giving, and never expecting anything in return, like the sun.
In this context, whenever we decide to sacrifice something or in modern language say to give up, renunciate or abandon a bad habit (smoking, drinking, slandering, control, even entertaining negative thoughts) and offer it in exchange of obtaining harmony, self-mastery, peace of mind, we already are on the path to greater joy and freedom. That represents a first step of going from ego to Self.
The next step is to make sacrifices for the well-being of someone else: I remember my sister giving up smoking during her girlfriend who had miscarried four times and was pregnant again. My sister really wanted to help her and didn't know how so I suggested she gives up smoking for her friend to carry the child through, and it worked. Her girlfriend gave birth to a healthy child and my sister never went back to smoking! Two benefits in one effort. Yet, there is a third level to sacrifice, one that implies seeking absolutely nothing as a personal benefit. Only very pure and disinterested Masters and Initiates have the awareness and ability to sacrifice something of themselves, even their lives, for the benefit of humanity.
Initiatic Science also teaches that every kingdom aspires to the next: the mineral to the vegetable, the vegetable to the animal, the animal to the human kingdom and humans to the angelic kingdom. Each category possesses qualities that are not given to the one below. The law of evolution invites us, consciously or not, to reach up to the next level. It is inscribed at the very root of life and in everything that exists. One way is to consciously transform our raw material into more sublime and subtler ones.
"The true meaning of sacrifice is the most elevated, most noble and divine manifestation possible."