The act of burning is a ritual practiced in almost all traditions which symbolizes many things but a common one is a gesture of ridding a past. Humans more easily identify this gesture with a physical act so they burn physical things which is not really lasting as we can always go back and get new ones.
Ritualistically, as with all journeys in life, we all have past that is no longer serving our betterment and I believe the nature of journey on the Camino provides the opportunity of uncovering those things...i.e. our wounds, anger, resentments and all the crap that we have been carrying throughout our lives. Coming to the end, we reconciled and let them go. We burn away those "thoughts", "beliefs", "ideas", "burdens" that do not need to come along on our new chapter after the Camimo. That can be done with mere intentions not necessary through a physical act of burning. Personally I see it as a great spiritual gesture (not the physical burning but the reconciliation as the end step).