The "unlimited storage" thing threw me. If I understand it correctly, it's limited by the free storage I have to use.
"Your computer quite possibly has hundreds of gigabytes of space..." actually, no. Yes, I have a desktop with hundreds of GB free, but my laptop fights with me every day to keep 10-20 GB free. In that case, I think a network file share makes more sense.
Aside from the confusion marketing, I like it. Definitely looks like a potentially nice, secure Dropbox replacement.
Also I don't fully understand the product from just the first page. Who is your target audience?