Used in Set Theory, Complex Analysis etc., The term in itself is not complete, since domain commonly can refer to any of two types of domain:

Domain of Definition: It is the domain that is specified for use. As an example, in complex analysis the definition of a function is: Let "S" be a set of complex numbers. A function "f" defined on "S" is a rule that assigns to each "z" in S a complex number "w". "f" is called a function and "S" is called the "Domain of Definition".
Natural Domain: It is the domain that is not needed to be specified but is naturally understood.
As an example for a function "f(z) = z/(z - 2)" here when the domain is not specified then it is natural to consider its domain to be "C \ {2}", since the function is not defined at "z = 2".