It is giving up something that you value. You can only sacrifice that which you would like to keep for yourself; in other words, that which gives you pleasure and joy. You cannot sacrifice something that you dislike or disown. Sacrifice is always related to a higher cause for a greater good.
At the same time, when your love for the greater good is so strong, nothing else assumes any value. Sacrifice here becomes irrelevant, because love alone is your strongest driving force. So, when there is so much love, there cannot be sacrifice. At the same time, when there is no love, there is no sacrifice.
For example, if a mother has made plans to see a movie and she realises that her child is sick, she does not say that she has sacrificed the movie to nurse her child, because she simply did not want to go. Nothing else seems to charm the mother besides being with her child.
When the love is lukewarm, then sacrifice assumes meaning. Yet, sacrifice purifies the human mind and reins in selfish tendencies. It can also bring pride, arrogance, self-pity and sometimes even depression.
You can sacrifice only that which you value. For a wise man, nothing is more valuable than truth, values and the Divine, and he will never sacrifice those. God is the greatest, and if he values the greatest, then how can he sacrifice God? This is the paradox of sacrifice.