By sacrificing an animal, we pledge that we would sacrifice ourselves in a similar way. Here sacrifice doesn’t mean to kill oneself. Sacrifice means to dedicate oneself, to devote oneself to God's cause. Devoting oneself fully to God's cause is real sacrifice.
During Hajj in Makkah, or on the day of Eid al-Adha at other places, we perform animal sacrifice. This is a lesser sacrifice, not the greater sacrifice. This animal sacrifice is a kind of ransom. By sacrificing an animal, we pledge that we would sacrifice ourselves in a similar way. Here sacrifice doesn’t mean to kill oneself. Sacrifice means to dedicate oneself, to devote oneself to God's cause. Devoting oneself fully to God's cause is real sacrifice. This is what Prophet Ibrahim did by sacrificing a ram in place of his son Ismail. Sacrifice of the ram was a lesser sacrifice. And settling Ismail and his mother in the desert was the greater sacrifice. Then a team of persons was prepared in that desert. This was a huge sacrifice. The desert was uninhabited, a place without easily available provision. It had no agriculture or horticulture. The desert had only mountains, open skies above and barren land below. This is where Ibrahim's family had to settle. There is no greater sacrifice than this. This was a living sacrifice. This is the sacrifice of Ibrahim's family. Imbibing the spirit of Eid al-Adha is what is really required of us on the day of Eid.