what are domain used for?

If a network domain is not define does in work, what are domain used for?

Yes a computer network can work without a domain.  Workgroup can be used for this propose. The main difference between workgroup and domain is how resources on the network are managed.  Domain refers to a group of computers and devices on a network that are administered as a unit with common rules and procedures. In a domain, one or more computers act as a server which is used to control the security and permissions for all the computers on that domain whereas in a workgroup no computer has control over others.
So, you can choose the option according to your requirements.