The "heavily decoupled" is a subjective qualifier, which basically translates to saying the source should be trusted to have a constant output. The method described for noise calculation probably assumes the voltage source does not contribute to any additional noise.
A "weakly decoupled" source, in this context, means a source which is prone to noisy outputs. This would negatively affect the noise assessment of the ADC.
The term "decoupled" is related to isolating the output from the mains power supply, or any possible adverse features from mains (e.g. voltage spikes), or any external interference overall. This is associated with the use of some common design methods, such as decoupling capacitors and overall board design.
For a mental exercise, pretend this is the output of a voltage source, with an inadequately picked decoupling capacitor. This could be a "weakly decoupled" source:
simulate this circuit – Schematic created using CircuitLab
While this would be a "heavily decoupled" one, in comparison:
simulate this circuit
This is just a silly example, decoupling concerns in real power supplies go beyond just output capacitors.