The city owes a "debt" to the past. This means that the city has developed and advanced from what it was previously. Earlier generations have done things which have made it possible for the city to be what it is today. Everyone owes a "debt" to the past.

It's a metaphorical debt, perhaps a debt of gratitude. Perhaps the people who lived in the city in previous generations did a great job of developing the city and the people who live there now are still benefiting from their work.