What does it mean to "believe on the Lord Jesus Christ"? (Acts 16:31). Here's an illustration that may help to answer this question:

Suppose you are sick and call for a doctor. After a thorough examination, he says you've contracted a fatal disease, but medical science has discovered a cure. You may be convinced that he is the best physician available, that his diagnosis is accurate, and that the medication he prescribes is your only hope. But you must take the medicine. If you just lie there and refuse the remedy, you will die!

So it is with God's offer of salvation. You may say you're sure that the story of Jesus is true, but if you don't reach out the hand of faith you will be lost for all eternity. You must personally receive the Lord Jesus Christ. He is the only remedy for your sins.

An elderly man in the hospital told a visitor, "When I became very ill and was taken to the emergency room, a physician I had never seen examined me. I could tell that he really knew his business. I had so much confidence in him that I said, 'I want you to be my doctor.'"

That's how we receive salvation. When we hear the gospel message and are introduced to the Lord Jesus, we must say, "I want You to be my Savior!"  — Richard De Haan