If you get this message and you still have free disk space, perhaps a lot of free disk space, then what follows might be your salvation.
Your problem might be that you have a file on your Dropbox.com site that is larger than the space you have available on your hard disk. This happened to me when a friend and colleague shared a folder containing a compressed archive of several VirtualBox virtual machine files. The archive file was 28 gb while I only had about 13 gb left on my drive. I kept deleting files until I had something like 22 gb, and Dropbox would still give me the same error.
Of course, once Dropbox raises the low-disk-space error it throws up its hands and stops syncing altogether. Other, smaller files that you may really want to get remain in the cloud. In my case those were a few relatively small photos that the Dropbox app on my iPhone had helpfully moved to camera uploads folder in the cloud. I was frustrated. Eventually (over the course of many days) I became very frustrated. Much Googling revealed many wrong suggestions, most of them from Dropbox themselves.
The solution: Simply use the Dropbox.com interface to download the offending big file manually to a different drive, and then delete it from Dropbox.com. In my case I downloaded the offending file to a usb drive. Relief was instantaneous. (I am refraining from making analogies here.)
I should say at this point that Dropbox works quite reliably and painlessly almost all the time. But…
There are some aggravating things about the driver interface (reached by clicking on the Dropbox icon on the task bar):
First among those is that the recently changed list, which is the main aspect of the interface, is worthless for diagnostics. The only way I found a clue to my problem was an evanescent image of a truncated file name like VirtualB…tar.gz presented once by Dropbox. This led me to search my Dropbox folder. No joy (apologies to Jerry Pournelle). Then a vague recollection of the file sharing popped into my mind and I searched the cloud. No joy. Again. But I eventually found it by brute force and in the process learned that searching for virtual on Dropbox.com will not find VirtualBox VMs.tar.gz but searching for virtualb will.
The other acutely aggravating thing (the interface is a chronic aggravation) is that the selective sync file list presented by the driver interface (usually a helpful feature, described here) would stop responding after one selection when the Dropbox workload was high (which it apparently is when it is obsessive about trying to find disk space for a big file.)
The other aggravating thing is that Dropbox themselves are wrong about the behavior of their software. They claim it syncs the smallest files first (which makes sense) but in my case the software seemed possessed by this 28 gb file and lost sight of the several 2-5 mb photos I wanted to get. Perhaps the system’s obsession was because the big file had been shared. Who knows.
The bottom line is that no one in the ether had published the actual solution to my problem. So, here it is for you.