Hi LaVonne, Manchester is near the Southern border of the old county of Lancashire, Burnley is to the North East of Manchester. I am not sure of how far it is from Manchester but in the days of your ancestor it would have been considered a long way. I have not researched this name, Ackroyd' but I am sure it is a North of England name. There may be Ackroyds in other Northern Counties too. Manchester, and other Northern cities, attracted people from the countryside who were looking for work,at the time of the Industrial Revolution, so the Ackroyds might have come from another place, but likely close to the city where they settled, as people didn't travel much in those days.
I found this on a website, I don't know if it is accurate but it is interesting:"the surname Ackroydmeans "dweller in the oak forest."