“Accepted partly” means that some records in the import did not change existing data or, in the Inbox form, that records were actively refused by the user.
The purpose of this message is to inform that some records did not change anything in the existing data. This is perfectly valid, but perhaps the intention was to update existing data and the Action = U was missing in the import file.
When importing data it is safe to use Action = U for all records. If the record exists it will be updated, otherwise it will be added.
Important: Always inspect the import result carefully before pressing the Accept button.