Parents bring their small children dressed in the style of the Child of Atocha (one of the manifestations of the Christ child) to participate in the procession in order to fulfill their promesa.

A promesa is a promise made by a supplicant.  The parents of these children made a promise to have their children participate in this procession as a show of gratitude for a gift given by God.  In this particular case, the gift requested was life--that is, each one of the participants was in danger of dying as a baby, but was saved, and in gratitude for their lives, they give testimony of their faith by participating in the procession.