If Adaptive is non-zero (the default), then area represented by the Region adapts to the new coordinate system. That is, the numerical values which define the area represented by the Region are changed by mapping them from the old coordinate system into the new coordinate system. Thus the Region continues to represent the same physical area.
If Adaptive is zero, then area represented by the Region does not adapt to the new coordinate system. That is, the numerical values which define the area represented by the Region are left unchanged. Thus the physical area represented by the Region will usually change.
As an example, consider a Region describe a range of wavelength from 2000 Angstrom to 4000 Angstrom. If the Unit attribute for the Region is changed from Angstrom to "nm" (nanometre), what happens depends on the setting of Adaptive. If Adaptive is non-zero, the Mapping from the old to the new coordinate system is found. In this case it is a simple scaling by a factor of 0.1 (since 1 Angstrom is 0.1 nm). This Mapping is then used to modify the numerical values within the Region, changing 2000 to 200 and 4000 to 400. Thus the modified region represents 200 nm to 400 nm, the same physical space as the original 2000 Angstrom to 4000 Angstrom. However, if Adaptive had been zero, then the numerical values would not have been changed, resulting in the final Region representing 2000 nm to 4000 nm.
Setting Adaptive to zero can be necessary if you want correct inaccurate attribute settings in an existing Region. For instance, when creating a Region you may not know what Epoch value to use, so you would leave Epoch unset resulting in some default value being used. If at some later point in the application, the correct Epoch value is determined, you could assign the correct value to the Epoch attribute. However, you would first need to set Adaptive temporarily to zero, because otherwise the area represented by the Region would be Mapped from the spurious default Epoch to the new correct Epoch, which is not what is required.
AST A Library for Handling World Coordinate Systems in Astronomy