What is a Christian? ‘Christian’ is the name that the people in Antioch gave to the followers of Christ (Acts 11:26). So a very short answer would be: A Christian is someone who follows Christ. Yet what does it mean to follow Christ?
A Christian follows Christ
First of all it means you trust in Christ. You trust Him to be your Savior. It means you believe you are a sinner, but Christ died for you on the cross and so He paid for your sins. He rose again on the third day and He is now your Lord. So a Christian does no longer belong to him/herself, but belongs to Christ the Lord. If you truly believe this, you also want to be baptized. Baptism is the mark that you belong to Christ.
In Romans 6:4 Paul writes about the meaning of being part of Christ, which is also the meaning of being baptized: “We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life“.
A Christian lives the new life
So a Christian is someone who died with Christ, but now ‘lives a new life’, because he/she is part of the resurrected Christ. That new life starts right here and now. That new life is something you don’t have to make yourself, it is a gift of God! You are being reborn through the Holy Spirit (See also John 3:1-21). And because you are reborn through the Holy Spirit you can now start following Christ.
Therefore Paul writes in the same chapter Romans 6:11-13: “In the same way, count yourselves dead to sin but alive to God in Christ Jesus. Therefore do not let sin reign in your mortal body so that you obey its evil desires. Do not offer any part of yourself to sin as an instrument of wickedness, but rather offer yourselves to God as those who have been brought from death to life; and offer every part of yourself to him as an instrument of righteousness”
A Christian wants to do the will of God
If you are alive with Christ, you will want to follow Christ and do the will of God. There is also still part of our old self which still wants to sin, but since we received the Holy Spirit and the new life through Him, we can fight against our sins and start following Christ. Therefore, a Christian is not without sin, but he/she will still try to follow Christ. And so we are back to where we began: A Christian is someone who follows Christ.
Get a good introduction about the Bible in What is the Bible?