Most small teams have a few basic needs: (1) team members need their important stuff in front of them wherever they are, (2) everyone needs to be working on the latest version of a given document (and ideally can track what's changed), (3) and team data needs to be protected from disaster. There are sync tools (e.g. beinsync, Foldershare), there are backup tools (Carbonite, Mozy), and there are web uploading/publishing tools (box.net, etc.), but there's no good integrated solution.
Dropbox solves all these needs, and doesn't need configuration or babysitting. Put another way, it takes concepts that are proven winners from the dev community (version control, changelogs/trac, rsync, etc.) and puts them in a package that my little sister can figure out (she uses Dropbox to keep track of her high school term papers, and doesn't need to burn CDs or carry USB sticks anymore.)
At a higher level, online storage and local disks are big and cheap. But the internet links in between have been and will continue to be slow in comparison. In "the future", you won't have to move your data around manually. The concept that I'm most excited about is that the core technology in Dropbox -- continuous efficient sync with compression and binary diffs -- is what will get us there.