One of the three primary factors of any genuine mystical or religious teaching, the other two being Birth and Death. Sacrifice describes the action of giving up self-interest in order to benefit others; it is also called charity, service, seva, altruism, generosity, etc.
"The blessed Krishna, the blessed Buddha, the blessed Lama, the blessed Mohammed, the loving, essential Ashiata Shiemash, Moses, Quetzalcoatl (and many others) were all avatars. The doctrine of all avatars has its roots in the three basic factors of the revolution of the consciousness: to be born, to die, and to sacrifice the self for humanity." —Samael Aun Weor, The Narrow Way
"Action does indeed bind the self [through cause and effect, karma] except when done as sacrifice; so work one must consecrated, offered to Deity high above. When beings came from Creator He ordained all to sacrifice; By sacrifice are worlds sustained And by it everyone does live. [...] Things exist through all other things, all things are knit with all others, so that the being of a thing is contribution by others. Independent no one exists as all are also all others, thus existence of anything is sacrifice by other things." —Krishna, Bhagavad-gita 3
"Only unselfish service, chastity, and sanctity take us to the ineffable summits. Now, sibling of mine, you have seen what the great service is. I know many spiritual brothers and sisters, good and virtuous, who fight for their perfection. I know many brothers and sisters who fight indescribably to correct their defects and to purify themselves. Yet, they do not remember others... They feel alone, they fight for their own spiritual progress and for their moral self-development. However, they do not remember that they have brothers and sisters, and that all of us are children of the same mother. Their spirituality is selfish spirituality. Therefore, the masters do not owe them anything. There is nothing to pay them because nothing is owed to them. They do not assist anyone. They do not sacrifice themselves for anyone, nor do they fight for the spirituality of anyone. Every initiation is a payment that must be given to the human being. Yet, if nothing is owed to the human being, then nothing is given to him. Therefore, even if he screams and cries out asking for an initiation, he will become old before receiving it." —Samael Aun Weor, Igneous Rose
In Hebrew, "sacrifice" is קרבן and comes from קרב meaning to "come close or draw near to God."
"The one lamb (Heb. keves) you shall offer in the morning, and the other lamb you shall offer towards evening" (Shemot 29:39 and Bemidbar 28:4). And about the secrets (Heb. Kavshi) of the Merciful One, the sages have taught: 'Why do you probe into the secrets of the Merciful One?', the meaning of which is: Matters that are of the mysteries of the world, let them be concealed under your dress. Just as clothes cover the body, so also must the secrets of the Torah be kept covered up, and this applies even more to the secret of the sacrifices, which are like a wife drawing near to her husband, which is what a sacrifice is called 'KORBAN', from the same root as the word kirvah, meaning nearness." —Zohar
"Jesus answered and said unto them, Well hath Isaiah prophesied of you hypocrites, as it is written, This people honor me with their lips, but their heart is far from me. Howbeit in vain do they worship me, teaching for doctrines the commandments of men. For laying aside the commandment of God, ye hold the tradition of men, as the washing of pots and cups: and many other such like things ye do. And he said unto them, Full well ye reject the commandment of God, that ye may keep your own traditions. For Moses said, Honor thy father and thy mother; and, Whosoever curse father or mother, let him die the (second) death: But ye say, If a man shall say to his father or mother, It is Korban [קרבן], that is to say, a gift (offering), by whatsoever thou mightest be profited by me; he shall be free. And ye suffer him no more to do ought for his father or his mother; Making the word of God of none effect through your traditions, which ye have delivered: and many such like things do ye." —Mark 7