The first gift of Christmas is a present Santa Claus gives every year on Christmas Eve. Every year, the Polar Express picks up children and takes them to the North Pole where Santa will pick whoever he feels is worthy enough to receive the first gift of Christmas, which can be anything of their choice.
One year, Hero Boy is picked for of his strong believe in Christmas (which he was very unsure about during most of the film). The hero boy decides to have one of the silver bells from Santa's reindeer. This bell was special as it can only be heard by those who have a strong faith and believe in the Christmas spirit. Typically, as children grow older they can no longer hear the bell (as they lose faith), but Hero Boy was one of the few who could hear it all the way throughout their life.