I'm not a native English speaker and I've read the descriptions in BOL but still can't understand what exactly are they. Can anyone explain in an easy understand way?
The screenshots from SSMS will help you understand the terms:
backup set - is a backup from a single, successful backup operation. E.g. a full database backup created at 8 AM yesterday
You can see that there are 2 backup sets in a single backup media set
backup device - a disk file or tape drive
backup media - tapes or disks where backup are stored backup media set - in the screenshot - it's the BAK file where backups are added
backup media family - You're creating the 8 AM full database backup and your database is huge, the backup takes more space than 4 tapes can store. Say you have 4 tape devices that are used to backup your database. When one tape is full, you insert a new one. If your database backup takes 20 tapes, that's 5 tapes per each tape device. The 5 tapes created on the tape device 1 belong to the same backup media family, as they have the same "father" - tape device 1