a workgroup is the name for a group of computers in a network environment. Under windows this is a name you can choose yourself for each computer. The computers who have the same workgroup name can easily exchange information through the network. A workgroup does not require a central server.
a domain is basically an advanced workgroup where every computer & user requires authentication (login/pass for instance), maintained by a central server(s).
workgroups are generally used in residential houses (for ex. to exchange data between 2 PCs), whereas domains are generally used in companies.