Tradition holds that a candy maker wanted to make a candy that would be a witness, so he made the Christmas Candy Cane. He incorporated several symbols for the birth, ministry, and death of Jesus Christ. He began with a stick of pure white hard candy: white to symbolize the Virgin Birth and the sinless nature of Jesus, and hard to symbolize the solid rock, the Foundation of the Church and firmness of the promises of God.

The candy maker made the candy in the form of a "J" to represent the name of Jesus, who came to earth as our Savior. It could also represent the staff of the Good Shepherd with which He reaches down into the ditches of the world to lift out the fallen lambs who, like all sheep, have gone astray. Thinking that the candy was somewhat plain, the candy maker stained it with red stripes. He used three small stripes for the blood shed by Christ on the cross, so that we could have the promise of eternal life.

Another description is as follows:

The Candy Cane, used during the holidays, stands as an important Christmas symbol. A candy maker wanted to come up with an idea to express the meaning of Christmas through the imagination of candy. That is when he came up with the idea of the Candy Cane. There are several different symbols incorporated through the Candy Cane. First, he used a plain white peppermint stick. The color white symbolizes the purity and sinless nature of Jesus. Next, he decided to add three small stripes to symbolize pain inflicted upon Jesus before his death on the cross and a bold stripe to represent the blood he shed for mankind. Two other symbols are distinctive on the Candy Cane. When looked at, it looks like a shepherd's staff because Jesus is the shepherd of man. Then if you turn it upside down, you will notice the shape of the letter J symbolizing the first letter in Jesus' name. These five symbols were incorporated into this piece of peppermint stick so that we would remember what we really celebrate the Christmas season.

Wikipedia covers the German origins:

In 1670, in Cologne, Germany, the choirmaster at Cologne Cathedral, wishing to remedy the noise caused by children in his church during the Living Crèche tradition of Christmas Eve, asked a local candy maker for some "sugar sticks" for them. In order to justify the practice of giving candy to children during worship services, he asked the candy maker to add a crook to the top of each stick, which would help children remember the shepherds who visited the infant Jesus. In addition, he used the white color of the converted sticks to teach children about the Christian belief in the sinless life of Jesus. From Germany, candy canes spread to other parts of Europe, where they were handed out during plays reenacting the Nativity. The candy cane became associated with Christmastide.