I think the white paper explains the idea of object storage quite well. I am not aware of any standard way to use object storage devices (in the sense of a SCSI OSD) from a user application.
Object storage is in use in some large scale storage products like the storage appliances of Panasas. However, these appliances then export a file system to the end user. It is IMHO fair to say that the T10 OSD idea never really caught momentum.
Related ideas to the OSD standard can be found in cloud storage systems like S3 and RADOS.
