Most of the information that I can find means nothing to users who haven't studied filesystems. What sort of advantages of btrfs are visible to the average user, without knowledge of how filesystems work?
Online filesystem defragmentation (Also, its a common belief that Linux needs no defrag. It DOES need sometimes. And there was a promised ext4 defrag but there is no sign of it. (Oy' Ted wake up (Maybe he saw the future and saw SSDs coming :>))
Compression (Guess its self-explanatory.)
Very fast offline filesystem check (Like fsck, just much faster (You know when you shut your PC down unclean and you have to wait quite some time to check it. Now, that will be done in a blink (or slower actually but still fast. :)) Who doesnt like that? :))
Online filesystem check (Maybe. Don't know how do they want to achieve this. Online fsck.. wouldn't be that bad.)
Writable snapshots (If there will be a frontend or something, then pretty much likely, everyone will be able to profit from this. Imagine something like System restore on Windows 7. Sounds good huh? Okay both in theory and reality it does much more than Windows. Uhm like time-machine in openSolaris, you can go back to dates and check out your docs back then. OpenSolaris (were) using the ZFS snapshots for this.))
Object level mirroring and striping (If you use mirroring or striping..)
You can join several drives/partitions into single filesystem. It's like mounting, but free space is shared, and files can be distributed across drives for speed.
For a normal user without knowledge of the filesystem (or how to manage it) the most important benefit is that btrfs (will eventually) be able to repair corrupt data caused by media errors and well as being more space efficient for some workloads. Since btrfs checksums both data and metadata (both the files and the filesystem itself) you as a user should not have to worry much about silent data corruption.