A workgroup is simple a grouping of workstations that do not belong to a domain. To some extent a workgroup can be viewed as a loose collection of machines doing peer-to-peer networking. There is virtually no security but it is very easy to setup and no dedicated "server" is needed.
A domain is a traditional network environment with a least one "server". A domain has, typically, one or more servers running Windows Server (e.g. NT Server, 2000 Server, 2003) or, for example, a Linux box running SAMBA. The domain not only contains servers, it contains workstations and workgroup machines. Security is controlled and administered from the server. Security on the network can be fairly tight. Thus it is much more complex to setup than a workgroup.
If you have a very small network, say under 5-10 machines, then a workgroup is probably the best way to go. Anything larger should have a domain; e.g. most businesses will have workstations connected to a domain for management of the resources by the System Administrator.
If none of the PCs/workstations are running 'server' edition OSs then a domain is not, in any case, an option.