The term Sync Library when used with an Apple Music subscription means that the music content and playlists in your library will be added to a cloud music library along with any existing unhidden purchases and available to any other computers or devices attached to your Apple ID where Sync Library is also enabled. Typically you can stream this content to the device, or download it so that it can be used offline. It is up to you exactly what content you download onto each device.
This is different from the practice of syncing content from your computer to a device over a USB cable, when all the content synced would take up space on the target device.
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