Dropbox keeps a replication of the data you have on their server, on your computer. So any change you make on your computer, is immediately made on their server. It is a wonderful service. Accessing files on your local computer will always be faster as the files are stored inside of your computer.
Files stored online first have to be retrieved before they can accessed. So for example, if the company (i.e. Carbonite) has their server in lets say Bora Bora, than your computer has to retrieve these files all the way from Bora Bora. Now, in the modern world this takes all but a couple of seconds, depending on the file of course, but it will still be faster on your computer.