Real belief is more than intellectual knowledge

Acts 16:31. . .”Believe on the Lord Jesus Christ and you will be saved; You and your household.”
Next to the infamous John 3:16 this is the gospel in one verse. To believe is to mentally acknowledge that something is true. Biblical belief, especially where the gospel is concerned, refers to mental acknowledgement + heartfelt devotion.

To believe in the Lord Jesus means that you acknowledge that He’s the only begotten Son of God (or God in human form if you understand the Trinity). That He came in the flesh to live a sinless life, die sacrificially for our sins on the cross, and resurrect after 3 days and is soon coming back to claim His church.

Heartfelt devotion is where you realize your own sinfulness (His atoning sacrifice doesn’t make any sense if you don’t realize that) and repent of your sins and commit your life to following Him as Lord and Saviour.

To “believe” is to rely on, commit to, surrender to, or give your heart to. And through His resurrection you can experience a new life free from sin if you invite Him to be your personal Lord and Saviour.