NAS in this respect stands for Network-Attached Storage - a NAS box is basically one or more hard drives connected directly to a network interface, with a rudimentary operating system to allow the file access.
Quite often nowadays the larger NAS boxes come with more than one physical disc and are configured in a RAID, so that if one disc dies the data is not lost.
Many NAS boxes come pre-installed with proprietary OSes, file systems and software, but I believe you should be able to install
FreeNAS on any NAS box, and this includes BitTorrent (as well as FTP, iTunes and others) capability
edit: on further reading re: FreeNAS, it seems it's actually for turning a normal PC into a NAS box, I don't think it'll run on a factory-built NAS box.
You may wanna try something like the QNAP TS-209 - the QNAP products feature BitTorrent support out the box and seem reasonably priced
http://qnapstore.co.uk/index.php?act=viewCat&catId=85