Once a schema change is made to a feature class in your geodatabase, you then republish the feature service using ArcGIS for Server. But that really does nothing for you in ArcGIS online. The ArcGIS Online web map will not reflect any updated schema changes if the web map is already created prior to the schema change!
This idea has been merged with Editing the URL path of a Web Map in ArcGIS Online.
You have to recreate the ArcGIS Online web map to see the schema changes. This workflow is completely unbelievable and impractical. What a waste of time, Esri. I hope you can change this in future releases.