Allow devices on the same LAN that have files already downloaded to sync the data between them rather than going through the servers to improve syncing speed.
This is especially important because:
a) Syncing speed is very slow (as mentioned elsewhere) because it doesn't pipeline well for many small files.
b) If I change my password I have to re-sync EVERYTHING. I'd be happy if that changes too, because it's pretty crazy to re-download 100s of GB just because of a password change. But if that isn't possible for the security reasons then at least the sync speed should be a lot faster.
LAN sync is a step in that direction. Basically LAN sync helps with big files, better pipelining/chunking helps with small files.