NP-34925-3 occurs if the PS4 fails to upload Game Save Data to the Cloud server while the console is on stand-by mode. The error will appear in the [Uploads] section of the [Notification] menu, usually indicating that save data failed to upload.
The PS4 Support site doesn’t specify exactly what error NP-34925-3 means, but according to the Prefix table, the error has something to do with the remote Network Server the PS4 is trying to connect to. It is likely meant to indicate that the remote server was unavailable when trying to upload the data, i.e. the PlayStation Network could have been down, or the PS4 could not connect to the server (connectivity issue).