Dropbox on a computer and Dropbox on iOS behave differently. On a Mac, (or other computer) Dropbox creates a folder that by default syncs ally our files. This means the files are local. On iOS Dropbox files are in the cloud by default.
In short. On a computer you have to tell Dropbox not to keep local files if you don't want them on the computer.
In iOS you have to tell Dropbox to keep files local, or they are only in the cloud and need to be downloaded each time.
So, when you preview a file on the Mac, you are looking at the file on your Mac. When you preview a file on iOS the file has to be downloaded first, unless it's one of the few formats that will stream; like audio or video. Word documents (.doc) can not be streamed, so they have to be downloaded first before you can view (or preview) them.