When a REST service is shared as an item in ArcGIS Online, the Service Description from the REST service auto-populates into the ArcGIS Online Description field. In fact, a number of fields that are published to the REST services automatically carry over to an entry for that service in ArcGIS Online.
However, when updates are made to the service description (on ArcGIS Server), the old information from the previous service description stays on the entry in ArcGIS Online. This makes it so a user not only has to update the information in the REST service, but they also have to go back in and either create a new entry for ArcGIS Online, or manually re-type in the information within ArcGIS Online again.
Since ArcGIS Online already has functionality to pull from the REST Service Description and auto-populate the description, the recommendation would be to enable an "auto-update" field whereby a user creating an entry within ArcGIS Online could be assured that any changes to description information within the REST service would automatically be updated in the ArcGIS Online entry.
For example, a service that is updated annually (ie. "Most Recent Imagery") which may include the dates included in the service would automatically populate changes the entry in ArcGIS Online if the checkbox was checked.
The checkbox would be preferred because it would also enable people to override the REST service description as well, especially when the service is not owned by the person creating the ArcGIS Online Entry.