Some papers (eg1., p. 2980) on isogeometric analysis talk about some geometric being exact or some geometry being expressed exactly.
The paper also says that
However, as NURBS patches (of higher order) are capable of representing most geometries exactly, ...
What does it mean?
This is one frequently encountered selling point of isogeometric analysis. For example, in finite element methods the boundary of a circular computational domain must be discretized using piecewise polynomials whereas in isogeometric analysis such geometry can be represented also in the discrete problem. This discrepancy between the original computational domain and the discretized domain is sometimes referred to as consistency error. If there is no such inconsistency then the geometry is said to be exact.
Thus, it means that the discrete solution truly represents a function defined in the original intended domain and not in a domain which is 'approximately the same'. It depends on the context what we mean by 'approximately the same' but you get the general idea.