CIFS doesn't have any filesystem size limits in and of itself. Sizewise it is limited by the server's access to internal storage only.
On the other hand, the server itself will have a filesystem limit (typically very high unless running old software) as well as file size limits. The clients might also have filesize limits that are smaller than that of the server. These all depend on the various versions of Linux, CIFS, and Windows in use on the server and the clients.
There are features that allow artificial limits to be placed, such as quotas - but these are peripheral to the original query.
As with @Sven, I have a 17TB Samba share being shared with various clients (Win8/Win7/WinXP/Ubuntu/Fedora/CentOS) with no filesize issues.
The 2TB 32-bit limitations seen elsewhere are to do with addressability. Consider a simple address example:
You tell a taxi you want to go to an address on a road with 150 houses (compare 3TB) but the taxi driver only understands numbers with up to two decimal digits (compare 32 bits - binary digits). This means the taxi driver can only deliver you to houses 1 through 99 (compare 2TB). You can use the road - but not to the full.
From the above, with a 3TB drive on an old system, it will only see the first 2TB of the disk. FAT32, for example, can only handle volumes up to 2TB in size and a maximum file size of 4GB. On the other hand, more modern filesystems can handle much larger sizes, far beyond the largest current physical disk sizes.
With CIFS/Samba, the scenario becomes a little silly - but nonetheless:
Instead of asking for the street and number, the taxi driver is really smart and simply asks for the name of the house (file) you want to visit. Then, instead of driving you to the house, he does all the hard work of figuring out exactly where the house is and delivers a copy of the house to you! Hence the size limits are based on how big a house you can handle, rather than how long a street.
The client computer never actually knows where on the server's disk the files are stored. It only deals with the actual content that the server sends. Thus the filesystem size becomes irrelevant to the user.