Leather buckets were a tool used in the bucket brigade method of firefighting. The colonists would have to get very close to the hot fire to throw the water on the fire. So, they used leather buckets instead of wood buckets, as leather did not ignite as quickly as wood. They also painted their name or sometimes a coat of arms on their bucket, to insure the bucket would be returned to them after the fire.
This graphic shows colonists using the bucket brigade method to try and put out a fire. This method was not very effective, as it was a slow process and it was dependent on a water source being nearby to have any chance of being successful.