What does it mean to be a Christian? What is the most important part of the Christian life?

A “Christian” is most basically a person who has a personal faith relationship with Jesus Christ. It means that someone has surrendered themselves to making Jesus Christ Lord and Master of their life. Being a Christian means that we have taken on Someone Else’s life. It means we have Jesus inside. This is not simply living for Him—it is living as Him. As Paul said so well, I have been crucified with Christ and I no longer live, but Christ lives in me. The life I now live in the body, I live by faith in the Son of God, who loved me and gave himself for me—Paul, Galatians 2:20. His loves, His passions, His perspectives become ours. And that’s what the world is supposed to see in us—a life and lifestyle and attitudes and actions that look like Him and sound like Him and act like Him. We are called to be possessed by Him. Therefore, we live to please Him, to grow in Him, to learn Him. The end game is not how much we know of Christ; it’s how much we show of Christ.
The term “Christian” comes from the Greek word christianos, which means “belonging to Christ.” Luke tells us where the term first came into practice; as he writes, The disciples were called Christians first at Antioch—Acts 11:26b. It appears that the term may have actually originated with non-Christians in Antioch as a term of ridicule. Over time, however, Christians took it over as a name of honor. Of course, it was from Antioch that the young church’s first missionary efforts, led by Paul and Barnabas, began. It was also at Antioch where Christianity began to stretch out from its Jewish roots, as a concerted effort led to Gentiles (non-Jews) first hearing and then embracing the gospel message of Jesus Christ for themselves.
It may be impossible to answer what part of the Christian life is most important. When one of the teachers of the Law asked which of the commandments was the most important, Jesus famously gave this answer: “The most important one,” answered Jesus, “is this: ‘HEAR, O ISRAEL, THE LORD OUR GOD, THE LORD IS ONE. LOVE THE LORD YOUR GOD WITH ALL YOUR HEART AND WITH ALL YOUR SOUL AND WITH ALL YOUR MIND AND WITH ALL YOUR STRENGTH.’ The second is like this: ‘LOVE YOUR NEIGHBOR AS YOURSELF.’ There is no commandment greater than these”—Mark 12:29-31 (quoting Deuteronomy 6:4-5; Levicitus 19:18). The teacher of the Law was impressed. “Well said, teacher,” the man replied. “You are right in saying that God is one and there is no other but him. To love him with all your heart, with all your understanding and with all your strength, and to love your neighbor as yourself is more important than all burnt offerings and sacrifices.” When Jesus saw that he had answered wisely, he said to him, “You are not far from the kingdom of God.” And from then on no one dared ask him any more questions—Mark 12:32-34a. Paul said this was a matter of “first importance”: Now, brothers, I want to remind you of the gospel I preached to you, which you received and on which you have taken your stand. By this gospel you are saved, if you hold firmly to the word I preached to you. Otherwise, you have believed in vain. For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, that he was buried, that he was raised on the third day according to the Scriptures—Paul, I Corinthians 15:1-4. To the Philippian church, Paul said, The important thing is that in every way, whether from false motives or true, Christ is preached.—Paul, Philippians 1:18a. Jesus Himself left His followers with these words: “[G]o and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you. . . . Go into all the world and preach the good news to all creation. . . . This is what is written: The Christ will suffer and rise from the dead on the third day, and repentance and forgiveness of sins will be preached in his name to all nations, beginning at Jerusalem. You are witnesses of these things. . . . It is not for you to know the times or dates the Father has set by his own authority. But you will receive power when the Holy Spirit comes on you; and you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth”—Jesus Christ, Matthew 28:19-20a; Mark 16:15; Luke 24:46-48; Acts 1:7-8.
To all this I would add growth—growing more and more into the image of Jesus Christ, the process the Bible calls “sanctification.” As Peter said, in some of the last words of his life, [G]row in the grace and knowledge of our Lord and Savior Jesus Christ—II Peter 3:18a. As we grow more into the image of Christ, that begins to make an impact on all the lives around us, resulting in more people asking us, as Peter said, to give an answer to everyone who asks you to give the reason for the hope that you have—I Peter 3:15a. To this you can add Bible study, to become more “versed” in the Word, and prayer, that daily never-ceasing communion with God. There are likely as many “most important parts of the Christian life” as there are Christians. But the most important issue for anyone is finding God on the throne of their life, which comes by means of a person’s surrender to Jesus Christ and then being seen by God as being perfect as He sees the perfection of His Son dwelling in their life.