One must understand the sacrifice, which is the essence of the occasion. A mother sacrifices sleep for her children. A father sacrifices his comfort for his children. Prophet Mohammed was himself an embodiment of sacrifice all his life. The sacrifice of the animals is just a ritual, whereas the essence lies far beyond.
A small incident from the life of Prophet Mohammed shows what sacrifice exactly is. Once the Prophet received a Christian guest from Najran in his house. There was no meal at night, except for some milk of a goat. The Prophet promptly offered him the milk. The Prophet’s family went without a meal that night although it had starved the night before as well. This is the right way to sacrifice for others.
Eid is also a day on which Muslims remember the deceased, visit the sick, see relatives and friends, overlook grudges and help the needy. They also show kindness and generosity to all those who they know. It is also a day for rejoicing and celebrating by getting involved in a good enjoyment and merriment.
Eid-uz-Zuha or Baqr-Eid, the festival of reminding one’s submission to God and the feeling of sacrifice and obedience attached to it, is also known as Eid-ul-Azha.
— Firoz Ahmed

