After Jack died, because he didn't believe in God, he couldn't go to heaven, and the devil wouldn't let him go to hell. In order to help Jack find his way back to earth, the devil gave him a burning charcoal. Jack put the burning charcoal into the lantern he carved with big carrots, which was the first "Jack's lantern" to help him find his way back to Ireland, but he never found it, so he always wandered around the world with the lantern.
In the ancient Irish legend, this small candle was put in the hollowed-out radish and called "JackLanterns", while the ancient radish lantern evolved to today, and it was made of pumpkin lantern. It is said that shortly after the Irish arrived in America, they found that pumpkins were better than radishes in origin and carving, so pumpkins became the darling of Halloween.