Hi,
It's both.
Basically, on each computer where you have Dropbox installed you have a Dropbox folder. This folder is mirrored "in the cloud" (on Dropbox servers) and on all other computers connected to your Dropbox. If you change a file on one computer it gets changed in the Dropbox on-line and on all the other computers connected to that Dropbox as soon as the "sync up".

If one Dropbox enabled computer is off the net you still have the files on the local harddrive in the state they where when the computer lost internet access. If you change a file on this computer the other machines will get updated as soon as this machine has internet access again. I'm not sure exactly how it works if the same file is changed on another computer as well.

Take a look at Dropbox website, they show you how it works.

/Henrik.