An address given for your ancestor could be the name of the town where he lived, the town where he received his mail, or perhaps the name of the township or county in which he or she lived with the word “township” or “county” omitted. It’s also possible that the location listed does not even exist any more.
Searching on contemporary maps, in local gazetteers, in county histories (see if they have maps included as well), in local newspapers, or in other sources may help you to determine exactly what the reference meant.
The man in the illustration lived in Appanoose Township at the time the document in the illustration was completed. Other contemporary addresses given for him–presumably also where mail could be addressed–were consistently listed as Niota, Illinois. It’s possible this reference of Appanoose is simply a one-off. It is not a reference to Appanoose County, Iowa, as the man in the illustration did not live in Iowa.