It depends on the data source and the kinds of edits being made.
When serving a map document, a schema lock is placed on the data referenced by the map, similar to opening a map document in ArcMap.
If attempting to edit a geodatabase you may get a message stating that the table/feature class is being used by another application/user, in this case ArcMapServer.
You will not be able to make changes to the database schema while the map is being served, such as adding a new field. Remove the map service to edit the schema; this is similar to closing any map document that references the geodatabase.
You can make non-schema related edits while the map is served, such as changing the value of an attribute or adjusting the geometry of a feature. These changes are reflected in the ArcMap Service.
See the ArcGIS Help topic "Schema locking" for more information.