If you want to display data in ArcGIS Online...
- With a public account (non subscription), you can add approximately 1000 features total from shapefiles or CSVs to a web map.
- If you have your own ArcGIS Server, you can reference your services as items and add them to web maps.
- If you purchase a subscription to ArcGIS Online, you can then host your data in ArcGIS Online, by publishing your map from ArcGIS Desktop or uploading shapefiles and CSVs to your My Content and creating web services from them.
Hope this helps,
Mike