An exact differential has the property that its integral over a path is path-independent: it does not depend upon the taken path, but only upon the origin and end of the path.
In mechanics, the work of a force can be path-dependent (e.g. friction), or path-independent (e.g. gravity), in which case it is also called conservative. When it is path-independent, the force can be associated with a potential energy, and the work is only the (opposite of the) potential energy variation; i.e. the difference between potential energies at origin and end of the path.
Work and potential energy (Wikipedia)
Then why the path-independent case was called "exact"? Probably because calculating the work involves no numerical approximation: it is the difference between two values of a potential energy, which has a known expression for usual forces such as gravity.
On the other hand, when there is a non-conservative force such as friction, its contribution must be calculated by an integral and may not have a closed expression, hence the computing should be numerical and give an inexact result.
See also https://physics.stackexchange.com/questions/603147/why-does-an-exact-differential-mean-a-force-is-conservative.