John 20:30  And many other signs truly did Jesus in the presence of his disciples, which are not written in this book:
31  But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.

Jesus Christ spend three and a half years ministering on  earth, proclaiming the Kingdom of God, and teaching them Who He was, by what He said about Himself ("Before Abraham was, I am"), and by the extraordinary miracles He did (healing the sick, raising the dead, feeding thousands with just five loaves and two fish), etc.
Everything He said and did moved toward one focal point: to provide them evidence by which they would believe that He was and is the Christ, the Son of God, so that believing, they might have life, through His Name.
Notice also the central place that His Name occupies in the plan of salvation.