You have posed a question which seems easy to answer, but rather one gets to learn more by answering the question. I am thankful to you.
What is Obedience?
Obedience is another word for respect which we show by listening and carrying out the acts unquestioningly to the command of someone whom we respect. That respect may arise as a result of fear, duty, love, etc.
In the beginning was the Word and the Word was with God and God was Word. So it is God's Word we should respect. The Ten Commandments. Or the teachings of Jesus. That should be an order for us. We should strive to obey them.
Similarly, we should listen to our elders and obey. We should listen to our teachers and obey. We should obey to our superiors in our workplace.
Obedience is a part of discipline. A disciplined life is needed for one to succeed. In one sense, obedience removes chaos and disorder. It ensures the chain of command. Disobedience means rebellion, mutiny, disrespect. Obedience in an organization is a must. Whether it be a small workplace, a school, a business, a service utility, a charitable organization or an army. Where the superior is the head and face of the body, the one who obeys is the arms and legs of the body. For a body to function properly it is not enough that only the head works. The arms and legs should act accordingly to bring the results. The head is the commander, the arms and legs the executive.
Whereas it is permitted in a family to question before obeying - as this may be part of a learning process -- in the army this is taboo. There the rules are FIRST OBEY, THEN QUESTION.
A person who obeys today, commands respect tomorrow.
One should obey and carry out the orders cheerfully and sincerely.
It is God who give us everything, right from the intellect, the sharp mind to the athletic body. So also without His Grace, Everything becomes Nothing.
Even for obedience to God, we should pray for his Blessings. This removes the arrogance and false pride in us and we learn to become humble and modest.
God Bless.